Just a bit of background: I have the first basic year of Music Theory down (took AP M.T. senior year of high school), developed a pretty decent relative pitch, have had a bit of experience with writing electronic music (trance, DnB) on a small home recording/editing music system. I've been seriously practicing advanced electric guitar technique for about 1.5 years now (learned a few basic things for a year or two before then), and now want to start improving my songwriting abilities. So on with it now...my question(s)...

My main problem is writing or coming up with chord progressions. I have no problem with melodies, counter-melodies, overall song structure, etc. But when it comes to the chords and basslines I get a little confused...

1. Do people usually write melodies or chord progressions first? Or kind of at the same time?
2. If two different chords both contain the particular note being played in the melody, how do you choose which one to use, other than by merely picking which 'sounds better'?
3. How do you come up with those weird chords that make you say "hey that's weird, but that sounds good"?

Sorry for the noob questions; I'm just really curious about songwriting these days. Thanks UG.
For number two, it really depends on the direction you want the song to take. A minor-based chord will darken things up a bit while a more major-based chord will lighten up the mood. A chord higher than the previous obviously tends to connotate (to me at least) a progressive pattern, while going lower seems to move towards resolving. But that's not always true. Mostly just what direction you want to take the song and what chord sound seems to complement the lyrics most.

For number three, those weird chords usually don't sound very good alone, but only in the chord progression! Also, alot of those "weird chords" are just alternate voicings of common chords.
Oops, forgot number one. sorry. I usally write lyrics first, then the chord progression, then the lyrics. And if you're not talking about vocal melodies, then instead of lyrics just settle on a mood and aim for that.
1. it all depends ... usually when i'm coming from an "i really need to write a song" angle i'll start with a chord progression, but more often than not i'll end up coming up with an interesting melody and i'll say "hey, i need to sit down and figure out a chord progression for that". usually, it's about half and half: i'll write a melody, and then come up with a chord progression for that, which becomes the chorus or verse or what have you. then i'll come up with a chord progression for the other half of the song, and write a melody for that subsequently.
2. it's up to you. you can even play chords which DON'T contain the note that's being played in the melody as long as they're in the same key. sometimes it even comes out better that way. alot of the time i'll use one chord progression over the melody in an intro, and then change the progression over the same melody for the verse or chorus (whichever i derived the melody from).
3. use a keyboard actually, if you have experience with a keyboard (i know alot of electronic musicians do) then use it. i'm a lead guitarist, and i don't use any other instrument when i'm performing but i find myself going back to the keyboard over and over again when i'm stumped about what to do next.