Get a corp with a crackhead contract to earn you dough while you're at it, too. After crackheads don't give you xp anymore, you'll want to try chuds/chobos who both live in the sewers. Beware, there's no cams in the sewers, so a grief-happy guy might try and attack you there.
Chuds do slashing damage, but other than that they're around the same difficulty as crackheads. Get snakeskin and some lotus armor, I guess.
Chobos are like upgraded chuds, except with pimped out pipes. They do beating damage like crackheads, but they do it harder and they'll be considerably tougher for newbies. Armordillo gear + HD will still probably be enough for them, just get at least 15-17 hit with your weapon? (dunno, it's been a long time since i was at that stage)
And then after THAT, try arachnos. They're in the subsewers below the bug queen. She does slashing damage and she's not too hard, but she has pretty good soaks and she will try and eat you. In that unfortunate event, light a cig and smoke it or if you have Writhing Smoke then just 'spew' and she'll vomit you out. If you don't have either, then you'll just have to die from her stomach acids/wait for a corpmate to cut you out. Keep in mind there's a nest there filled with bug eggs that you can sell to Avram for a good chunk of money. They're also used in the BrundleChud quest, and they're a trophy too!
On to the actual arachnos: these beasties are tuff and buff like you've never seen before. They have small soaks, but the main problem with them is that they do a truckload of slashing and stabbing to the unprepared newbie. I would advise having 20+ hit on your weapon to deal with them. In all honesty, for defense, when I was a newbie I just got snakeskin and layered leather jackets + pants, got a riot helmet, layered lotus tebukuros, and got a pair of combat boots to defend against their attacks. (They also have parry class 2 pincers, so only player characters with parry class 2 weapons will be able to parry them! People with parry class 1/0 weapons will have to rely on dodge.)
There's so much after arachnos that I won't even bother to list them here, but what I did was yetis in the mountain pass (they can powerattack), ice yetis in weezer (they do unsoakable psychic damage), karnivores in nukem academy (they do a FUCKTON of bullet damage, get caballero gear for these guys!) and then bootleggers in Glowstiller (they can either do a FUCKTON of bullet damage (even more so than karns) where you need caballero gear, or they might have melee weapons like sledgehammers/chainsaws/baseball bats etc.) which is where I am currently right now. If you need help just page 76Moogle in game.
EDIT: @ thebmw, HD actually defends against 3-5 beat damage which is more than the untrained fist does, but crackheads still might score a 1-3 damage hit against you. Get some lotus gear just in case. They won't hurt you at all with armordillo gear on.