I'm just too impatient. I've been playing this game for 24 hours now but I still haven't learned not to rush anything xD
Rushing is totally viable!
Like I said, it's hard to give basic tips, but here are some Invisible, Inc. "principles."
1. Your chief enemy is time, so you do want to move as fast as possible. That means sprinting when it's safe and covering as much ground as possible each turn. Splitting up your agents is usually a good idea until it becomes clearer where objectives and the exit teleporter are. Then you may want to reunite them, because they're much more effective at taking out enemies and holding down an area as a team.
2. Try not to engage the enemies until you have to. It's rare that you'll ghost a map — just because of all the things conspiring against you — but as soon as you take down that first guard, things will start to unravel and the alarm level will rocket upwards. Hold off taking someone out until you have to (they spot you, or you can't lure them away from your chosen route). Exception: on early missions, if you can't steal from guards yet, you may want to knock out and loot everyone you see, just to build up some funds.
3. The most important thing is to survive each mission. You will not clear most maps 100%, and you definitely won't clear the later maps on harder difficulty settings. Learning to leave safes and other loot behind is a learned skill. Recognizing when a situation is about to spiral out of control and bailing out is a learned skill. Focus on the mission objective and the exit teleporter. Everything else is icing.
4. The most important mechanic is cover. It isn't immediately intuitive where you're invisible to guards (although it's improved in the release version, as it now shows holes in their vision), but once you understand how it works, you can squeeze through very tight spots in a turn or three. Drawing enemies' notice (yellow question marks) is absolutely fine; they'll investigate and then return to their patrol if they don't spot you. You can use this to draw guards away from important locations, too. Red exclamation marks mean the level is starting to go sour; guards don't go back to their patrol once they've spotted you even once.
5. Being spotted isn't game over. You get a free move of one space, and if that takes you into cover, you won't get shot. So if you understand how cover works, you can start to intelligently position your agents at the end of each turn in ways that let you bail out safely even if a guard surprises you. This lets you plan for the unexpected and be much more aggressive. This is kinda hard to explain without diagrams, but start thinking about the room you're in, imagining what the worst possible thing that could happen next turn is, and positioning your agents accordingly.
6. You can't really plan your builds. Certain agents work better with certain equipment, programs and augments, but a huge part of the game is adapting to what you're given. Just like Risk of Rain or FTL, you may find a really powerful item or upgrade early on and have to tailor your playthrough to fit it. A big part of the game is fitting what comes your way to your chosen agents' skillsets. There are some very powerful synergies out there, but usually you will have to make do with something suboptimal. Usually, that's more fun.
7. Choosing missions is important. Are you struggling to generate power or hack effectively? Go for a mission that gives you Incognita programs. Are you short on cash? Hit up a vault. You may also want to factor in travel time (because the more missions you squeeze into each day, the more chances you get to build up cash and upgrades before the finale), difficulty level and corporation. That last point is important: if you don't have good hacking yet, you do not want to go into a high-level Sankaku building. Trust me.
8. When making purchases, prioritize armor piercing. You will likely not survive a run without at least one character who can take down armored guards. They start to show up on level 3 missions and above. You need to stay ahead of that curve to be effective, so grab the augments and items that help.
9. For the most part, you want to have cash on hand. Keep 600+ on you at all times, because you may never know what you'll stumble over in a store on the very next mission or what Monst3r may have for sale at a discount. Don't burn all your money on agent upgrades unless you're overflowing with cash or are about to start the final mission.
10. The best agents to use in the beginning are the starting ones: Decker and Internationale. Decker is fast and has a get-out-of-jail card in his stealth ability; Internationale makes managing cameras and consoles simpler when starting out.
11. The most powerful upgrades in the game are a third and fourth agent, so rush Detention Centers where possible. The agents you rescue won't have their starting augments and equipment, but they let you cover more ground, they're invaluable for pinning guards in tight spots, and you can use them as bait or distractions.