I currently have 4 planets under control. I have three AI controlled on my borders.
That suggests you are building a tightly packed contiguous empire. On low difficulty levels or some map types, that can work. However, before you get too far in, I should caution you that if AI Progress gets "too high" (a very context dependent threshold), the game will become very hard, possibly even unwinnable. During the very early game, taking adjacent worlds may be necessary. Just be careful not keep taking worlds without a reason better than "It's adjacent to my empire."
Two level III and one level IV. On one of the level III worlds, it's heavily mined, was packed with Mark III bombers, forcefields, various heavy hitting guardian types and that was just when I put a scout into the system to see what was there. It also has an advanced factory and an ion cannon. I desperately need the AF, but between the mines and the cannon, I cannot come up with a strategy that doesn't cost me most or all of my forces. And they brought in a carrier with 250 ships on it last time I played. Is this the usual AI systems I am going to have to fight?
Are you sure you need the Advanced Factory right now
? As long as you do not own it or cause its destruction, it will sit there waiting for you. With only 4 worlds, you probably have not captured enough Knowledge to unlock many high level designs. If I recall the game mechanics correctly, an Advanced Factory is only useful to you once you have unlocked a Mark III ship type, at which point the Advanced Factory will let you build a Mark IV of that ship type. If your empire is like I expect, you have few or no Mark III ship types, so that Advanced Factory will gain you almost nothing for now. Later, once you have the spare Knowledge to unlock more Mark III types, then the Advanced Factory will be valuable. AI War requires you to pick your battles, and this battle may be one you should avoid for now.
One way to deal with mines is to use units with Mine Immunity. Such units can drive across a mine field without triggering it. Assault Transports are immune to mines, and could be used to carry your fleet into the system without triggering the mines. Ion Cannons cannot fire on units with Insta-Kill Immunity. All starships, and some fleet ships, have this. You could use starships to destroy the Ion Cannon in an initial raid, then bring in/unload your fleet ships.
A carrier with 250 ships seems a bit heavy for this early in the game. What is the type of the non-enthusiast AI? What difficulty level did you set for each AI?