Wow, FTL is hard as dried corn! I'm getting my ass handed to me on Easy, can't even make it through the second star system map yet.
I meant to respond to you earlier, but the road to hell is paved with unbought stuffed dogs. Thing is, there is a MAJOR learning curve to FTL. For a game that seems rather simple, the strategy can run very deep. It's not a controlling strategy, by which I mean that you can't simply load in whatever you'd like and then push into the unknown; it's a strategy that starts with understanding what you've got, and then taking the best advantage of that in every possible scenario.
As an example, in some (many) runs it's very hard to stock up on crewmates. If you're in one of those games, you won't need to buy a crew transporter; in fact, in the early stage of learning the game, the transporter seems a little trivial. But once you find yourself with a couple of unattached crew members, ideally of the mantis persuasion, the transporter is an amazing resource. You'll have level three sensors by then, of course. So when you find a ship with a minimal crew, you can take a few early shots and then transport your crew over to defeat the enemy in hand-to-mandible combat, which gives you way more resources.
And then if you happen to have the same setup but with a couple of Rock crew members to spare, you'll see the deadly combo you can play with the Fire Beam, if you can find one of those: take down the enemy shields, transport the Rock crew members into the weapons room (say), and use the Fire Beam to ignite the weapons bay and whatever is nearby. Rock aren't harmed by fire, but the enemy will be when they come to fight you. At this point, any ship whose shields you can take down is yours to plunder.
There are so many of these combinations - the more you explore, the more you'll learn. Also, the FTL wiki is a pretty good resource. My thinking is you should stick with Easy - it's a very hard game - until you win one against the Enemy Boss. Then try surviving on Normal. Good luck!
I have to say, this game is brutal even on Easy. I never seem to have quite enough money to upgrade and recruit as much as I need. I got to the third star map tonight, but once again was thoroughly decimated by a boarding party. I'll likely give the game a few more tries, but then it may be back to Don't Starve or Risk Of Rain again for my masochistic gaming. :)
You are meant to Pause all the way through battles; remember that you are controlling not only multiple systems, but also the actions of several crew.
Boarding: one of my first purchases in most games is to upgrade the Doors subsystem. The best place to fight boarders is in your Med Bay: best general strategy is to have your doors at level two (or three), move your crew as much as possible to the Med Bay, and then vent the rooms where the boarding party is to vacuum. As they pound through the Blast Doors, they'll take damage; then you can meet them while they're in a weakened state. Often they'll die before they can get to you anyway. The better your doors, the more they are slowed down.
Also, that Alien Spiders event is almost always bad news. If I don't have a Cloning Station, I won't do it.