Sounds like the attacks you're seeing are almost exclusively Threat. You should do what you can to avoid provoking it; attacking guard posts or tachyon posts without killing the things you wake up is a really good way to get a lot of threat very fast. Keep a close eye on the threat warning at the top of the screen, and put scouts on enemy planets at least 2-3 deep from your territory...you'll want to check the galaxy map for threat on a regular basis (that's one of the dropdown options and I think it defaults to shift-T, or maybe that's something I configured on mine), so you know where it might come in from. If threat gets to be more than a hundred or two you should consider proactively attacking their threat ships. Threat hits you where you're weak, so compare that threat number to your defenses on any planet that borders AI territory...if you'd lose a planet if that many ships attack, then they probably will attack. Otherwise they bide their time.
You mentioned deepstrikes...yeah, don't do deepstrikes, or at least don't keep your ships in deepstrike-level territory unless you're going to pull them back REALLY fast. If you're trying to hit a DC or co-processor, seriously consider scrapping your ships as soon as they've killed their target. Threat builds up by the second when you are deepstriking. That, and seriously do NOT underestimate how much stuff you'll wake up by just hunting tachyons. Every once in a while I decide to send some raid starships or a wad of cloaked things to exterminate like ten or twenty planets' worth of tachyons in one go, and every time I do it, I lose the game almost immediately. You'll wake up a bunch of stuff and it'll join up with Threat as soon as you leave. Doing that on Mk.IV planets is suicide. Be careful--you don't even need to be deepstriking to screw yourself over this way. If you really really want to scout things out but you can't clear a path without a lot of deepstrikes, consider 1) loading scouts into a full cap of assault transports and planning to lose a whole ton of them, and 2) find a planet really far out in the direction you want to scout that you'll want to keep later in the game, even just as a chokepoint or something with a lot of metal, and capture it early. That'll push back the range of what's considered deepstriking, and will let your transports hop a lot farther before dying of attrition. Just remember to be careful what you wake up!
Now, threat can't quite come from ANYwhere. If you have captured a lot of territory but there's a lone AI planet somewhere in the middle, not connected to the rest of their space, gate raiding (and maybe neutering) is entirely sufficient. Threat from elsewhere can't get there, so you don't need to significantly defend against attacks. Once you gate raid it, as long as you stay out you can pretty much ignore it...maybe sweep through once every few hours to clean out their ships, but otherwise you're fine. You probably don't even need force fields on your command stations that only border an isolated and neutered planet, because there's just not much they can do with it at all.
