Well, let's see...
Penicillin: Penicillium crysodigium, a mold. There are dozens of penicillin derivatives (ampicillin, amoxicillin, bacampacillin, carbenicillin, piperacillin, and a host of others) that are either produced by fermentation using appropriate substrates for P. crysodigium to turn into a penicillin analogue, or by chemical modification of the basic structure.
Cephalosporins: Genus Cephalosporium; I forget the species. Isolated from a sample of sewage from Sardinia. ALL cephalosporins are chemical modifications of the native molecule; the technology producing the first usable cephalosporin (Keflin; it was IV only. Keflex was the first oral one. Others cephalosporins include claforan, omnicef, ancef, spectracef... and lots of others...) was developed by Eli Lilly and company when Glaxo (the company that found the stuff, and realized it was horribly toxic in its native state) couldn't whip the process.
Macrolides: Erythromycin, clindamycin, lincomycin, darithromycin, clarithromycin, and others. Chemical modifications of a basic structure that I think was bacterial in origin.
Aminoglycosides: Bacterial origin, I think. Gentamicin, netilmycin, tobramicin and others. Terribly toxic, and not used a lot.
Tetracyclines: Don't recall, but I think these were bacterial too. Dozens of variants on the initial tetracycline molecule: minocycline, oxytetracycline, chlortetracycline, doxycycline and others. Again, all chemical modifications of the initial structure
Sulfonamides: Totally synthetic. There's dozens of 'em! Sticks in my craw we just stumbled over the basic structure then elaborated on it.
Trimethoprim: Totally synthetic. It was designed to inhibit a particular enzyme unique to bacteria
Floroquinolones: Totally synthetic. Ciprofloxacin, levofloxacin, gatafloxicin, moxifloxicin, and others. This one is a "designer" antibiotic, too; DNA gyrase from bacteria (there are lots of different kinds, almost one for every species) was isolated and characterized and the molecule was designed to inhibit it. Turns out that a lot of them inhibit topoisomerase 4, too.
There are other groups, but this should get you up and flying.
If you want some real deep goodies, go to the library and check out Goodman and Gilman's textbook on pharmacology. It's huge, and it'll give you more than you'd ever want...