Actually, the Greek testament in the KJV is just as bad if not worse than the Hebrew section, Rachel. Bart Ehrman has written an excellent critique/expose of the KJV and other Textus Receptus-burdened editions. The Greek section has plenty of anti-Semitic, anti-women, anti-pagan slurs. I’ve linked to his book on my blog.
FWIW, Dave, you could check out the New KJV (NKJV), which is an edition that had changed a lot of the errors and crap that were in the KJV. I think the poetry is intact, however, and like you, I find the poetry very important. I like the Jerusalem Bible, despite its rather clunky British-English translation from the French.
I agree, too, with Karl, that funerals are for the living, not the dead. However, if a Biblical section is associated with the deceased and it helps invoke his/her memory among the living, then go with it. My wife, who is a minister and has presided at umpteen funerals, aims for whatever will offer comfort to the mourners. As Karen said, there are those verses that, in a ground zero sort of situation like a funeral, do just that. Most of us leave our heads at the cemetery gate, so to speak: we bring our hearts and these words speak to them.
If I may throw in something more that’s slightly tangential here: if you don’t want to burden your survivors unnecessarily, plan your funeral even if you’re 20 something–you can always change the plans if need be. Plan the music you’d like, Bible verses (or Qran or whatever), pick somebody to do a eulogy, etc etc. The less survivors have to try to plan something in such a difficult time, the better for them.