Go for biome quality over biome quantity. Embarking on four separate biomes doesn't help if all they generate are foxes, deer, marmots and mountain goats. You also get more animals on a larger embark.
Tropical moist broadleaf forests seem to have the widest array of species (
http://df.magmawiki.com/index.php/DF2010:Forest#Tropical_moist_broadleaf_forests) for a land biome, but I haven't checked them all. Tropical anything, actually, seems to be better, because that's where the rainbow of monkeys are. Savagery gets you the giant versions of lions, tigers, etc.
Keep in mind you'll have to mod almost all of these cool animals to be [PET] instead of [PET_EXOTIC], and that the wiki lists are not complete... f'rex, you get jaguars in any tropical and presumably giant jaguars in any savage tropical, but they're not listed on that master list for a tropical broadleaf forest.
Oceans/lakes also have a CRAPLOAD of animals, if you're up for getting them out of there/possible desalination.
Pay attention to relations with elves, even pre-embark--pretty sure you trade with their nearest civ, and you get what they have access to. There is nothing more disappointing than having those pointy-eared bastards bring you donkeys and horses and MULES. :[
Trapping the caverns isn't a bad idea, either--generate a world where the caves have more twisty passages than open spaces, drop clusters of cage traps at chokepoints, and have doors/emergency airlock bridges set up for FB time. (If you want more headroom, I think the minimum reqs. for titan attack also apply to FBs.) Keep in mind that a lot of underground creatures will make a beeline for your fort--a trapped tunnel leading to a forbidden door that can be bridge-blocked with a lever is like a magical magnet for voracious cave crawlers/crundles/giant cave swallows/bats/rats/pretty much every single C2/C3 creature.
Stockpile space/designations and the animal housing are what gets me every time.
Unless things have changed in this version, animals will give birth while caged, but won't conceive more litters. They have to be tame to breed. (Worth finding out: do sieging animals knock up tamed ones, like wild animals do?)
Owned tamed animals wander around after their owner, doing vile things to your FPS, while stray tame animals on chains keep generating paths that they'd
like to wander on, using up valuable PC power before the chain tells them that no, you can't go there. I believe one-tile pits are popular. I'm going to experiment at some point with restricted-traffic meeting areas to keep critters in their pits/1-tile cells with pet-forbidden doors.
So: Tropical savage jungle, shrubland, and ocean/lake would be my suggestion. Alignments can be nice, but good doen't give you many more creatures, and evil means you have to test-embark to make sure you get fantasy-evil with werewolves, instead of wasteland-full-of-zombie-deer-evil. (Also werewolves are a pain in the arse.) Mountains would be a plus, but not strictly necessary. Also, see what animals the starting civs in your world can offer you. Muskoxen and camels, afaik, you can only get from elves or trapping after embark.
...Can you tell that a passion for building a menagerie has been the death of many of my forts? ;P Updates please when you start, for !!science!!?