Tolerable AIP levels vary rather dramatically with a number of factors so it's hard to give particularly strict rules. In a typical sort of game you expect to capture up to 20 planets, with the associated AIP increases. If you're doing Fallen Spire, then AIP is much less of a concern; you are recruiting alien allies which allow you to much more directly confront the AI. 2000+ AIP is not unreasonable if you're doing that.
Going over 200 AIP in a non-Fallen Spire game triggers a mechanic where the AI will begin redirecting some of the strength used to spawn defensive reinforcements into waves. The redirection is penalized on difficulties below 10, though, so this shouldn't be a huge problem at Diff 7. At diff 7 you could probably handle 300 AIP with decent defenses, and I wouldn't be surprised if you could handle 400 AIP for a short period (ie, between killing one AI homeworld and tackling the next). Yes, even as a new player, if your defenses are at all competent. You can see my defensive set up in my AAR, which was at Diff 10 with lots of player-friendly cheese:
http://www.arcengames.com/forums/index.php/topic,15770.msg175890.html#msg175890Everything is harder on higher difficulties, though. All of the AI's responses scale faster with AIP on higher difficulties; they get more reinforcements, bigger waves, and will launch larger CPAs. You also get less AIP reduction from data centers at high difficulties.
The typical number I've heard is about 20 planets taken at the end of the game. Depends quite a bit on map size and layout, obviously, but that's a good rule of thumb.
I would try to avoid taking large swaths of territory. Consider hacking fabs instead of taking them, this can save both the AIP for taking the planet AND the need to defend that planet for the rest of the game. This is especially useful for fabs that would be hard to defend. ARS systems you can abandon after you cap the ARS if you don't want to hold them. You can travel up to four hops out from any non-AI-held system without triggering deepstrike responses, but you don't have to hold planets you clear for that purpose.
If you can take an advanced factory, you may want to unlock MkIII scouts, at which point the factory will grant you the MkIV scout. You only get one and it's slow, but it is immune to tachyon, making it uncloakable and effectively invincible, so you can use it to scout the entire map, then park it on an AI homeworld.
I think most people tend to focus their K into upgrading their mobile military, especially their bonus ship unlocks, favorite starships, and bombers. You don't need to upgrade your whole military, just the important stuff. IE, if you get a fleet unlock that doesn't have any bonuses you need, leave it at MkI.
Area mines, grav turrets, and HBCs are really solid defensive unlocks. At diff 7 you proooobably won't need a huge amount of defense. Target your turret unlocks for whatever has the bonuses you need, if you need to pick up turrets to supplement defenses, but you may not need any MkII turrets. Core Turrets (which count as fabs for hacking purposes) are also great defensive options depending on the turret.
Ideally, set up your primary core such that there are a few choke point systems that you control that the AI has to pass through. When a CPA shows up, you want the ships to have to fly through at least one choke point to get to anything vulnerable, and you want those chokes heavily defended. That's also where you want your waves hitting, so that the same defenses that kill waves can also be used to kill CPAs.
Kahuna is very turret-happy but he plays on Diff 10 against difficult AI types. You will not need as many turrets at Diff 7.
