Behemoth- You asked for recommendtions on death and black metal bands, so you would probably like the entire spectrum of their music.
Carcass- I personally love every album these guys have released, but you could purchase their Choice Cuts album, find the songs you like on there, then find what album those songs are on, and purchase those albums.
Decapitated- This is another band that I love every album, this band in fact, is probably my favorite death metal band, period. But Winds of Creation is probably their best work.
Immolation- This is another band that I could easily say every album. This bands production has gotten better as their albums went on, Harnessing Ruin's vocals are more audible, bass and guitar parts are clearly heard on Unholy Cult.
Meshuggah- Destroy, Erase, Improve
Overkill- This band is so constant, always putting out albums every couple of years, and good ones too. So many of their older albums are so kick a**, but personally I love Horrorscope, for newer albums I cannot get enough of Necroshine.
Vader- This band is so underrated, also from Poland like the other band you inquired about Decapitated, but they have been at it for way, way longer. Their late drummer Doc was the answer to what a death metal drummer shold be, but was never mentioned alot when the topic of best drummers was brought up. Older albums, Black to the Blind, Sothis (see Doc shine on this), newer, Litany, Revelations. This band may be my second favorite, I can't say enough of how awesome they are
Death Angel- Frolic Through The Park, let me tell you I must have listened to this album hundreds of times when I was in high school, and it is a thrash metal landmark.
On a personal note, my friends here in Central Oregon have an awesome death metal band named Desolation, check them out at
www.desolation.info. Their web page has a link to their MySpace page, that has three or four songs from their new album Crucifucked, that was recorded by Vile's Juan Urteaga. They have toured with Deicide, and just did a small tour of their own for the new album. They are originally from Louisana, your neck of the woods, and are honestly some of the cooliest guys you could ever meet. If you do check these guys out let me know what you think.