Hi, CareyB. Are you playing your game in turns or simultaneous? If in turns, do you use strategic combat or tactical? Simultaneous games won't let you do tactical, but you can click the replay combat button when you get a combat log report, to see what happened in the combat, and try to figure out what went wrong.
Dropping mines in warp-points as you expand helps slow down any hostiles who might try to follow you home, at least until they start researching mines themselves and using minesweepers.
I hate the Evil Empire thing, but you can easily switch it off in settings.txt - just open it in a text editor, do a Find for evil, then change the value for "AI Uses Mega Evil Empire" from True to False.
Picking strategic systems to defend is important, controlling routes into your most developed systems - even better is to try to keep the fighting in the other guy's real estate.
I'm pretty much of a newbie, too. One thing that has worked well for me (against AI at least) is to research fighters as early as I can, and then base most of my combat ships on the Light Carrier until I have researched my way up to something better. The Light Carrier is big enough to let you use a good mount for your direct fire weapons (to increase range and damage), plus even if you only go with the minimum required number of fighter bays that gives you room for 28 small fighters. The Light Carrier can even be a pretty decent assault ship for planetary invasions, loading up with shields, PD, and a couple of cargo bays to add capacity in addition to what you get from the fighter bays (I usually cram these so full of troops that they don't have room for any fighters, but the bays are still there to give you some flexibility if you don't need a full load of troops).
Hope this helps.
SpaceBadger
PS: Merry Christmas, y'all!
