Not exactly a "n00b" question my my definitions, but its certainly something you could've found on your own.
In any case, Advance of Zeta is based in a time period before
Stardust Memory 0083 and
Zeta Gundam. You're missing quite alot of general information just by not seeing either of those series, as the Advance of Zeta story fits in-between them and "bridges the gap" for those two series. Theres plenty more story information I could go on and on about, but I'd be here for awhile.
In regards to your "Can I use a GM, Gouf, or Zaku" question is simple to answer though. Firstly, you might like to take a look at the AoZ Wiki>
http://aoz.numinalabs.com/index.php/Main_PageTheres plenty of information there. Go the Category "Mechanics" under the Titans Test Team. There you'll find an alphabetized list of Mobile Suit images and profiles.
Really, the Advance of Zeta story focuses on the military group "Titans", a faction of the EFF (which you should be familiar with from 08th MS Team) who's purpose is to clean up Zeon Remnaints from the OYW, so technically you could use that Gouf and that Zaku as Zeon Remnaints forces. The Titans Mobile Suits, as you'll quickly find out from looking at the Wiki, are designed off of Base models like the GM and the GM Quel, as well as lots of prototype transformable Mobile Suits that can be found in
Zeta Gundam.
Your knowledge of 08th MS Team can help a little bit as far as Zeonic designs go, but the SEED information is useless here, as its all in a different timeline/century.
