@cwilder
Buddy, I thought you were gonna spend much more time in
black metal country, first

before wading into
death metal. But hey, you really can dive into both genres, simultaneously.
There's a whole bunch of different sorts of top-drawer dm bands that I have already named on this thread. And now Symptoms has posted a very good list of his own.
You mentioned Bloodbath. Ace band, no kidding. I think even devstorm cited them in the Opeth thread. In the Swedish dm scene, Bloodbath is one of my few favourites. All their three albums and an EP, while sounding somewhat samey-samey here and there, are nevertheless excellent death metal worth any fan's time and money. There's a very recently-released DVD,
Bloodbath Over Bloodstock that I've got and quite enjoyed.
wilder, if you like Bloodbath, you really ought to also check out
Vomitory. That's another equally cool Swedish heavy-hitter. There's just loads of swell dm on offer, that I'm spoiled for choice making recommendations for beginners. But you could either choose to begin with the old-school masters like Cannibal Corpse, Morbid Angel, Malevolent Creation, Obituary, Deicide, Vital Remains, Bolt Thrower and others, or get into much newer contemporary bands. One band that pops to mind that I think you'll readily like is Poland's
Vader. In any case, you must listen to the pioneers of the genre to really get a genuine feel and affinity for what death metal really means, and how it's evolved over the years, to this day. Once you're hooked, there's no going back.
edit: belated B'day wishes to Symptoms. And if it isn't too much trouble, Symps, I'm kind of really curious to know what are your most favourite albums (name just one) by each of the bands you just listed above.