To get military-grade equipment, assault military-grade ships, duh. Laser weapons are very commonplace at weaker military ships, mutant pogroms and space, and, of course, supply ships.
To get power armor parts: fight traders' guild. The better is (their) ship, the more dudes in power armor you'll get, and if lucky, you might even face a guildmaster! And again, you can raid supply ships, if you're willing to brave the nukes.
Also, power armor is totally unnecessary until the very endgame (I talk about Cydonia, unless you're insane enough to go with mere spacesuits instead. I wasn't). You can do just fine with guardian suits; they hold their own against most threats well.
You won't be able to shoot down all the enemy ships until the lategame, since them scurvy dogs sometimes will send a bomber, destroyer, cruiser or a freaking battleship to sniff you out. You can, however, shoot sentries and fighters and loot top-tier Space Rangers' laser pistols! They're pretty good.