I'd suggest bomber starships, raid starships... basically starships
Whatever the strongest individual units you can muster are, and pack in as much as you can without triggering the eye, and just kill the guard posts one by one (probably will take several tries). Alternately go over the cap but still only bring ships that will contribute, and stuff all the hard-target-killing stuff into a few transports and rush them over to the targets and unload (if you have supply I think you can just scrap the transports, but it may be not-on-hostile-planets-at-all for that); most of the stuff on the planet will chase the other loose stuff you brought in and your heavy-hitters can get in the most damage.
Ultimately if you have a strong enough defense to catch the AI Eye's backlash you shouldn't have to worry about it too much. If they all stack up on a wormhole waiting for you there are lightning warheads to smash them (at AIP cost, true).
And I'm sure folks around here have much better strategies.
Also, if I buy the expansions (Which I definitely will) will it make the game easier?
It depends. TZR, maybe. CoN, kind of 50/50 depending on how much you like throwaway attack ships. LotS almost definitely not, those new bonus ship types are an object of hatred once they fall into the hands of the AI
Though we have toned them down quite a bit.
Each gives you new toys, but also gives the AI new toys. If you play with something like "Broken Golems - Easy" or "Spirecraft - Easy" that definitely will make the game easier, but if you play the hard variants of either the AI will definitely give you a challenge to go with the superweapons.
Ninja'd. Twice.