sp00ki

you just made my head hurt...

ok, i'll try:

3/32 or 1/8?
depends. track specific stuff tends to be 1/8, but there's a lot of stuff out there in 3/32 as well. The typical rationale is that 1/8 is more durable, but 3/32 is lighter. doesn't matter which you use in the long run as long as you remain consistent. ie, if you go 1/8 your cog should be 1/8, as should your chainring and your chain.

if you're looking for a "flat top" type bar, just go with risers or flat bars (these will be mtb, typically).
Your best bet is to look for a 25.4mm quil (threaded) stem and pair it with a pair of 25.4 risers (type 25.4 mtb riser into google and you'll see why). if you need the drops, that's easy too-- again, type 25.4 road bars into google and you'll find tons. Bullhorns are the same thing. you have lots of options here. stick with 25.4 to keep things simple.

brake levers
depends on the bar style, of course. since you want to spend time on the flat, cross or bmx levers are probably your best bet. i like the tektro style cross levers, as they're light and simple. low profile and reliable, nice and strong. they also come in lots of sizes, so make sure they work with the bars you buy.
if you're used to hoods and wanna go with drops, that's an option too. you already know how that works, though... tektro also makes affordable road levers, but there are zillions of others.

Cranks
this depends on how tall you are, but most people opt for 165 when riding fixed in the street. in fact, "track" completes all come with 165mm cranks (the idea is that there's less risk of pedal strike when leaning into turns as you're forced to pedal).

style is something you're going to have to learn yourself. some people like (for whatever reason) brooks saddles dispite their being tacky, heavy, outdated monstrosities. others demand track specific parts, some people hate the look of carbon, some think aerospokes are cheezy, etc. etc. etc.
there's lots of ways to find what you like.
if you're concerned with asthetics and want to find inspiration, check out fixedgeargallery.com.
there's lots in there, going back for years, so you'll be able to figure out what looks good to you and what doesn't. there'll also likely be a lot of functionality type stuff you haven't considered before, so keep that in mind too.

here's a quick list of what you need:

frame/fork (you have this)
quill stem
headset (must be 1" threaded)
handlebars
brake lever
brake (and cable, of course)
wheelset, tubes, tires (if you live in a city, go with something durable like gatorskins or hardcases)
bottom bracket
cranks
pedals w/ retention system
chainring
chain
cog/lockring
seatpost
seatpost clamp
saddle