Hi Dreamer and welcome!
AMG stands for Aufrecht Melcher Großaspach,
and is a company owned by Mercedes which Adds More Go. They do a number of things like make wheels and body panels but the main thing is they make hand-made engines and generally tune up the car. The web site is www.mercedes-amg.com
and has got some great pictures and videos.
From your post I'm guessing you're after the original 'R170' models, made up to 2004. The 'R171' models made after that have different numbers and look quite different.
An SLK32 AMG looks like a 320 but: the engine has a got a metal 'waffle' on top, the wheels are a special double-spoke design, there's a little curved-up lip on the boot as a spoiler, twin exhaust pipe which says 'AMG', there are some other body changes, the doorsills and speedo both say 'AMG', the boot says 'SLK32' on the left, and 'AMG' on the right.
The 230 is a lovely car, as is the plain 320. The 32AMG is a lot faster and the acceleration is just delicious. I think the most comfortable one is the 320, the zoomiest one is the 32AMG, and still think the 230 is great. Personally I think the 200 is underpowered. The 'facelift' they did in 2000 made some good changes to the steering, but is most visible in the indicators in the wing mirrors.
Did you know you can get a manual 230 or 320? They're a lot of fun too. If you're fussy about the colour you might like to know it's pretty difficult to find an AMG in anything other than black or silver.
In the end it's a question of personal preference. Why not go drive a few and see what you think?
Hope that helps
PS: this post has some nice pictures of a 32AMG
And this one has a picture under the bonnet: