Missiles at low tech levels (below an average of TL3) are generally quite useless, even at ships with their own tech level. Beam weapons are here much cheaper and useful in general.
At TL3 I would say that ASM becomes useful with decent speeds and yield to combat ships.
At TL4 you will generally be able to afford research into ASM and AMM technology and make them very effective. It is also at this level that I generally start to seriously consider fighters to replace smaller missile ships as the major capital ship combat platform.
These consideration are certainly much more apparent in multi-national games where you control more than one faction, but even against the AI I find this approach to be the more logical and realistic approach. The reason is because you need both the research, industrial and wealth infrastructure to support larger and more complex ship systems. You need research into many branches and you can start to diversify quite allot at TL4 and above. Before this most of fleets will be defensive because most opponents will be more advanced (or at least slightly better) than they are, deploying missiles in that environment is rather futile.
As to sizes and missile types then there are many variant of missiles doctrines that you may approach. An ASM can generally be anywhere from size 3-12 and can come in many shapes and sizes.
Larger missiles will generally rely on armour, high yield, long range. They will generally be slower, easier to detect, but cheaper to produce.
Smaller missiles will be faster with lower yields and better suited to hit faster ships, preferably with less armour.
I find that medium sized missiles at about size 5-6 on fighter platforms will give me a nice offensive fire-power against larger enemy capital ships (they will be fast and powerful with a short range), while I reserve size 3-4 for frigate sized and below ships to combat each other. Size 8 (25% reduction) launchers will be my general purpose missiles launchers that I fit on destroyers to combat either larger ships and/or their escorts. The launchers can be fitter with missiles of size 4 or 8. Size 4 will be a MIRV kind if missile that separate directly after launch. These missiles is a nice mix of good yield and range. Size 10-12 (25% reduction) launchers are fitted to large cruisers/battleships/battle-carriers and will be viewed as artillery missile batteries.
I rarely put active sensors on my main missile ships that can target out to my missiles maximum range, such sensors are simply to large and expensive. I instead rely on a smaller backup sensor and smaller scout ships (500t or below) to paint my targets. These smaller scouts can easily be deployed at TL2 and above. This will also reduce the chances of the enemy actually knowing when and where a missile barrage will come from and hopefully even protect the missile ships from even being detected at all. This will obviously not always work.
I try to aim for any ASM to have about 80% chance to hit an enemy ship. This obviously depend on the enemy ships speed. The maximum power modification of missile engines I use will usually be 4x or higher. Lower mean better range higher mean harder missile to shoot down and a missile that can track faster ships without adding manoeuvrability to the missile.
A good standard size 4 missile template is 50% engine, 25% warhead and 25% fuel. This give you a good balance of speed, range and hitting power.
In a fighter launched size 6 missile I would have a 3 MSP engine, 1 MSP fuel, 2 MSP yield.
In a size 8 medium ship missile I have about 3.5 MSP engine, 1 MSP armour, 1.5 MSP fuel and 2 MSP yield. This missile give me a decent speed and range, good protection and good yield.
On a large size 12 missile I go for a 5 MSP engine, 1MSP of armour, 3 MSP of fuel and 3 MSP of warhead. This give you a very high yield, some protection and a very good range.
You should also observe that a missiles yield will become even more important in version 6.30 of the game, especially at higher tech levels, perhaps starting at TL4-5 or so I think.
