hi there =)
I really want to help you out and explain this game to you, but i honestly don't know where to start. It's so huge and complicated that even experienced players like us get overwhelmed sometimes. Luckily there's a lot of good and experienced players who lurk these forums from time to time so everything you need to know will get answered properly eventually.
First thing you got to know is that there is not one specific way to play this game. Many different tactics and strategies can work. That being said, your options become more limited the higher up you go in difficulty and there are some basic rules that will always prove to be a guide in the right direction.
I've learned that the most important thing in this game is to stay in control of things. Of course depending on the options and settings you've turned on, there will always be chaos in the galaxy. But the more things you control, the better it will turn out for you.
First off there is neutering.
I consider warp gate raiding, destroying guard posts and killing off most of enemy forces on a planet to be part of neutering. Neutering is what you do to keep control of things. You go to every single world that's adjacent to one of your own and you take out all the warp gates, except one. By leaving one warp gate active, YOU decide where all the regular waves will come from. Keep in mind that objects such as eyes (sentry eyes, parasite eyes, etc), alarm posts and warp gate guardians also count as warp gates. Pick out a world of which you assume you will never have to take or a world that you think is way to difficult to take yet or something like that. Pick out a world that has only 1 wormhole leading into your territory. Fortify that single wormhole. Even if your fleet is lightyears away, a good turretball can hold off an incredible amount of enemy ships. My personal choices are tractor turrets, gravity turrets, Heavy Beam Cannons, Lightning turrets, Flak turrets and maybe sniper/spider turrets depending on the situation. Place the turrets in range of the wormhole but as close to your command center as possible, since that's the enemies most likely target. Get higher mark heavy beam cannons if waves are becoming challenging. Use your other turrets to protect your other planets (just keep your homeworld better protected than the rest). Always use grav/tractor turrets. I personally always forget to use mines but they can come in real handy too.
Don't just take out the warp gates, leave the wormhole guardposts alone but take out all the others. The less places the enemy has to build up forces, the easier it will be for you to keep their numbers low or travel through their space.
Attacking structures like warp gates and guard posts (or even just moving around in their territory) will "wake" Ai ships from their fixed positions and they become part of a group called "threat". Threat ships will stalk you and look for an opportunity to attack anywhere, so take them out before they get a chance to do so. Always keep an eye out on your threat count. In many cases, threat is more important than AIP. If a CPA or exo wave just spawned, hover over the word threat and find out exactly where they are coming from (assuming you've scouted properly, but more on that in a bit), follow their movement and divide your fleet/reserve turrets accordingly. You'll gain control over the seemingly randomness from the CPA/exo this way and it will help a great deal.
Don't confuse threat ships with Special Forces. The SF roam around and protect worlds they find important, often surprising you with large numbers. They only show up in AI/neutral worlds, either protecting something or just passing through. They will never attack a world that is already yours.
Next there is scouting. If you play with extra fog of war and show unexplored planets off, you'll learn to scout manually properly, like i did.
At the start, you won't be able to scout much at all. Mk I scouts are useless (1-2 hops at best usually) so in order to find a proper target i usually unlock mk II scouts right from the start, but they'll only get you so far. Once you got a little bit of spare knowledge (and no proper target to take over anymore) you'll unlock mk III scouts and also mk II scout starships (250 knowledge only). Then you put all of them together, mk II + III scouts and mk I + II scout starships. Make them group move using g+click or g+control+click to move them through a wormhole. Manually maneuver them to avoid as many enemy ships/structures as possible when they come out of a wormhole. Always leave the most damaged scout of the lowest mark behind, before you move on to the next world. You leave a scout behind so that you will always know what's going on in that world. Never leave the starships behind, because they'll help your group survive longer. First time you do this you should be able to scout at least 10-15 worlds in a 7/7 game.
I'm not sure i can help you with economics since I have a different playstyle than most people. I never build economics stations. Never. I upgrade my harvesters to mark III from the start of the game and for the rest i build logistic command stations everywhere. I don't skip planets to keep my AIP low, I scout for a target and then capture every single planet along the way, doing all of the above. I rely heavily on reducing enemy speed and increasing my own, creating fastways on key connections using Zenith Space Time Manipulators. My fleet will be wherever it needs to be in no time. In a 100 planet galaxy, I usually take 30 to 40 planets. With so many worlds, both economy and knowledge is hardly an issue. Of course I have to adjust my playstyle a bit for most AI types but it works in general. I'm no 10/10 pro, but i can beat easy/medium AI types on 9/9 (haven't tried hard types yet).
Steamrolling can still work, it just takes a different approach.
Hacking can be a very useful tool. You can hack all sorts of different things. You can hack an ARS (Advanced research station) to choose out of 3 different ship types. You can hack an AI back-up server to either prevent the AI from ever spawning a particular ship type again or to take that ship type for yourself. You can use the hacker to gain extra knowledge from worlds that you don't control or you can use it to sabotage certain annoying AI structures.
You can do all sorts of fun stuff with hacking, the only problem is that it costs points called Hacking Progress Balance. Basically your HPB is the same as your unreduced AIP (so if you have 100 AIP and destroy a datacenter, your AIP will go down but your HPB will still be 100). Hover above the words Hacking Progress Balance and you will see some info about how much HPB you've spend and how much every individual action costs. Each time you use a hacking action, the price of using it again will go up. The more points you've spend, the stronger the enemy forces that will spawn while you hack. If your hacking balance goes below 0 because you hack to much, the enemy retaliation will be severe, possibly more than you can handle.
Using the Super Terminal to reduce AIP also costs HPB. So spend your hacking points wisely.
There is so much more to be said about this game, but I'm done for today. I'm sure you've heard a lot of this already but I just wanted to cover some stuff that's been important to me and I hope I've still been of some help =)