1. what is a good active-sensor setup?
The way I generally do this is to make a "Watchship" class of ship that takes care of all of my sensor needs. It has:
Several layers of armor in the early game, as this will be the ship that gets targeted more than anything else. In the mid-game I'll add some shielding to this.
Enough engines to keep up with the rest of the fleet.
Large passive sensors, of each type. There are a few things I use baselines for this. Can I spot my enemies' engines from far outside of engagement range? Can I sense their Active Sensors before their Active Sensors would sense me. Would I be able to sense an inhabited planet with a thermal/EM signature of a small colony from far outside of either of our weapon ranges? Those are all of my goals, but depending on tech level I may not be able to attain all of those goals. When push comes to shove the Active Sensor capabilities of the Watchship are more important, each passive sensor probably shouldn't take up more than 10-15% of the ship's volume.
Now we get to the Active sensors, the easiest one to plan is the AM sensor. I give it a range of 150% that of my AMM missiles and ship Fire Control. That way the AM ships can stay ahead of the rest of the fleet by a small margin. In the very likely event that all of those missiles are heading for the sensor ship that will give the defenders another few salvos at the missiles as they fly past.
Everything else should be the ship active sensor, and it should have capabilities that mesh with those of your missiles and FCs.
2. what should I be using to defend any 'non-sol based' colonies?
There are many, many different ways to do this. As you mentioned building a carrier it seems like you are going to have fighters. A few Hangar PDCs stocked with Fighters/Gunboats are a great way to put some defenses on the front line, especially for smaller colonies. Once the colony is large enough to support some Maintenance facilities you can switch over to defensive Frigates, or tug in some orbital stations.
Of course those ideas are more of a self-supportive way of looking at the colonies. Another perfectly valid way of looking at it (especially from a roleplaying aspect of a government skeptical of the Colonies' need for having control and the ability to support firepower). Is to just make small fleets of ships that go to the colony systems for 3-4 year tours before returning to Earth for refitting.
