Hovering over your HaP display at the top of the screen will tell you the current costs for all available hacks. Each successful hack increases the cost of another hack of the same type by 50%. The display also shows how much you've spent on each hack to date.
The AI's response to hacks goes up with every hack. Having a lot of excess HaP available will reduce the response somewhat, but there is a minimum response that goes up with every hack. If you try to hack at negative HaP, the AI response goes up very dramatically; the farther you go negative the worse the response gets, and it's very nonlinear.
Thematically, as you capture planets and otherwise anger the AI, you're also uncovering backdoors in the AI's programming that you can exploit. However, when it detects those backdoors being used, it attacks you and works to close them. The more backdoors you've found, the less the AI notices you using them. When you're out of HaP, you're basically brute forcing the AIs code, which is super obvious and makes the AI rampage against you.
Fab hacks are very popular, since hacking a fab means you don't have the capture the planet AND you don't have to defend the fab. They're also super reasonably priced.
Factory and ASC hacks are pretty expensive, but potentially worth it if they're in particularly indefensible spots.
Design Download hacks are solid gold, if there's a very strong ship type available and you have the K to unlock higher marks, as they get you an entirely new ship type. They're not cheap, though.
Design Corruption hacks are nice if there are any ships that you just don't want to deal with. Most useful against ships that are a threat in waves; the hack will not stop Mark V versions from showing up on the AI homeworlds. Eyebots are a good example, as a wave of eyebots is a pain in the butt.
Sabotage hacks are nice for getting past otherwise unwinnable defensive combos. Guard post that wrecks bombers under a FF? Sabotage the FF. It's also great for AI Eyes, since the hack response will up the number of ships in system, and the eye itself is a valid target.
Haven't found much use for Sensor hacks yet.
K hacking is a great place to spend spare HaP, you can always use more K.
I think the new system wound up being a nerf to Superterminals, since you'll run out of HaP at some point and you have to trade off against other uses. Still potentially extremely valuable.
From a design perspective, hacking is intended as a sort of anti-RNG. You can't use it to solve all your problems, but you can use it judiciously when the RNG throws you a really awful situation.
