Hello, as a fellow newbie I understand your frustration.  I recently lost a 30000 ton beam ship to a few gunboats with box launchers, they were the perfect match for my ships.  But later, I ambushed 10 of them on a jumpoint and after that used missile fighters on another group.  My missile technology is horrible, but I had intelligence on the range and resolution of their sensors and was able to close in unseen, most of my missile missed but I could rinse and repeat, the AI neither escaped nor tried to find the source of the missiles (a bit disapointed there) and kept guarding a jumpoint untill I finished them all.

I think you are almost at the top of the learning curve or at least about to reach a less stept part, don´t give up now!

I feel for you.  Ok...self advertisment here, read my AAR.  Especially read the battles.  They were one sided slaughters up to the last one which is closer to a roller coaster ride.  To engage higher tech ships with lower tech ones is possible if the lower tech ships have missiles, with beams forget it.  For the beam weapon to be effective (and this is true in starfire as well) you have to be able to dictate the engagement range.  If your ships are slower they can't do that.

Beam armed ships fulfill secondary (but often vital) roles in Aurora but they aren't and, due to the nature of the game mechanics, can't be primary weapon platforms.  To put this in starfire terms, the most advanced beam weapons have a maximum range of 1 hex, while the most primative missiles have a range of 10 hexes.  Using AAMs in AS mode you would be at around 2 m km to 0.05 m km at the lowest tech levels.  At higher tech levels even AAMs can have ranges of >20 m km while a beam weapon has no more than 1.5m km.  The only arguement against missiles is that you have to build them and put them in colliers.  So it is possible that a missile armed fleet exhausts their missiles before the destruction of the enemy force.  It depends on a lot of other factors at that point what that means strategically.  But beam weapons aren't just shorter ranged as is the case in starfire they are only viable at ranges so short it reduces their value to certain particular and specific circumstances.

In starfire due to the way the rules are made you have limits to the technological disparity you can face, in aurora they don't exist with respect to certain NPRs.  In starfire terms you just ran into a race with Xr, and SBMs while you have T1 destroyers.  You would not even see the ships destroying your fleet unless the enemy chose to allow that as well in starfire under those circumstances.  Same same if you run into a race with SBMHAWK while you are T7 or fighters while you are T6.  How many T2 races are going to survive an encounter with a T5 NPR battle fleet?  Ind2 vrs T3 would also be a one sided slaughterfest.

In aurora the one stat that rules them all is speed.  It needs to be changed but so far as I know it isn't in the pipeline to be changed.  Missiles doing 10 pts of damage probably are moving at 20 000 km/s or more that means they cover 100,000 km in 5s and due to the way final movement is handled you are denied an interception chance.  You need to deploy small craft with missile sensors or else build a bigger dedicated anti-missile sensor.  But first you need to figure out how fast those missiles are moving.

The ships will be destroyed.  It is not your fault, it is not the wiki's fault it is just the fact of the matter.  Everyone who has played this game has lost ships due to the technological difference you can face.  If you want to avoid their destruction activate the SM tool and move them out of that system, outside of that pray the NPRs run out of missiles.

About the only thing you can do now is disperse your ships and hope that by spreading them out one missile sensor will be able to pick up the inbound missiles far enough out to give you warning to allow your ships to engage.  Your beam weapons have the range to mutually support even with the ships seperated by 50K km.  Though only by using a slow tracking beam fire control.  That is my only suggestion that I can see working, and it certainly might not.   Spreading your ships out might allow you to lock up the missiles though, keeping all your ships a km or so appart won't cut it.

Yes, your problem are the sensors which are way, way too weak. You can't see the missiles because they are too fast and they hit you before you see them. I would keep playing if I were you, but only if you accept that it is a learning game that you might very well lose. If not, better restart, maybe with the spoilers races unticked.

Hey, I kind of lost a few games already. Remember, Losing is fun

That said, I strongly recommend you to browse the bureau of ship designs forum, and maybe even post there what you'd build before actually committing to that. It sucks to discover in the field that your designs are crap. Like I did

Ahh, the failures I was able to accomplish

Honestly early game tech isn't too crippling against vastly more powerful foes, you just need massive tonnage Advantage, and ships that are pure sensor platforms in order to spot anything. Of course researching size 20 sensors would take some time.

Active Search Sensor MR0-R1 (1)     GPS 10     Range 500k km    Resolution 1

Your anti-missile sensor has a range of 500k km against a size 1 target (20 space missile).  For a 6 msp missile the range would be ~56,000 km which means the fastest missile you can see with this sensor is ~9,200 km/s  which is rather slow.  I would look at updating your sensor to a range of 2m km which would give you a minimum detection range of 220,000 km which would detect up to 37,000 km/s missiles. 

It appears that since you are still using nuclear pulse engines after 14 years game time that you started conventional or with very limited research.  The NPR players do not have this handicap, they start with TN techs and good research ability, at least until they overbuild and cut research in favor of maintenance.  If you are going to start with such a great handicap, you should wait to explore out of your home system until you have researched some advanced technology. 

The Wiki ships are not great designs or even adequate designs they are tutorials on how design works.  The Bureau of Ship design or the Aurora fiction sections are a much better location to get sample ship designs for a variety of tech levels.  Steve's fiction is particularly good in showing multiple design philosophies and he does a test campaign for each version of Aurora so that you can see the effect of the specific rules each version is using.   

To use your Starfire example, what you have done is like starting a campaign at industrial while all of the NPR's are starting at TL 3 and then complaining that the game is rigged against you.

A couple of other points. 
You aren't picking up the missiles at all since you got no intellegence information on the size of the missile.  Two targets also threw a salvo of 19 scale 10 warhead missiles at you.  That is probably 10 missiles from each ship (1 missed).  If the missiles are moving fast (something you can figure out by the range to the ship and the time between salvo impacts) this can suggest the tech difference you are facing.

200 for a thermal rating is pretty low when you talk about military drives unless they are using thermal reduction technology.  You might be facing gunboats with box launchers.

Your beam armed ships need to have their weapons assigned to beam fire controls.  The beam fire controls need to be in one or another of the point defence modes.  I would suggest the ship being shot uses final fire mode while the others go into area defence mode.  Others will suggest alternatives but unless the fire is spread out between your ships let them try to support each other.

As has alread been stated you need a ship with a sensor that can pick the missiles up far enough out to give you a chance to engage.  My guess is that you started conventionally and that your technology is only barely TN.  That means that you are going to loose lots of ships to things you can't see.  Even if you can see them though, your fire control has to be able track the missile sufficiently well to engage it.  The ratio of the your tracking speed to the missile's speed will modifiy your chance to hit.  So if the missile is coming in at 24000 km/s and your tracking speed on your firecontrol is 2000 km/s your chance to hit is divided by 12.  Even a point blank range last ditch defensive shot (~80-90% chance to hit) will be reduced to around 5-7%.

I'm not sure what tutorial you're following so here's a mini tutorial, you need resolution 1 sensors to detect missiles, there's a few ranges listed when you design a resolution 1 sensor, range vs 50 ton object or larger, Range vs size 6 missile or smaller, range vs size 8 missile, and range vs size 12 missile.
Generally you want the range vs size 6 missile to at least match the range of your antimissile beam weapons, or the range of your Anti-Missile Missiles, however in practice you want at least one ship in your fleet to mount a sensor capable of detecting missiles at a much longer range. Also note that theres a 10,000 kilometer minimum range for sensors to detect anything at all, and also a more practical minimum is 6 times the speed of the missile you're trying to intercept, which is the distance it will cover in a single 5 second increment plus one additional second , if your sensors don't have at least that range you won't pick anything up until it's hit your armour.
Note that any ship you control can use it's sensors for lighting up targets, what your defencive ship needs to have itself is a fire control of the right resolution and range to actually fire it's weapons at the incoming missile.
I believe for final defencive fire a 10,000 km fire control is all that's needed. I'll go through the procedure for final defencive fire in a minute.
Edit: Thx Charlie.

thanks for the reply, I managed to work out how to turn actives on while I still had six ships.

no difference, I can track nothing until I get an event saying it hit me.