For a fast start I tend to like the fast-fighter types - raptor, space plane, raider etc - you can spec em up to II or III and get a full complement of high level versions more or less straight off the bat without running into terrible energy or resource issues.
Micro-fighters and bulletproofs aren't significantly better than normal fighters IMHO so I don't tend to pick them.
As for ship selection against various types I don't think anything is really mandatory - you can always research starships and turrets as needed to match up...for example if you are against a Force Field happy AI then I would definitely get some Raid Starships specced up...