I have looked everywhere and have come up with nothing. Is there a one
piece self contained piece of equipment which is not really expensive
(I haven't even found an expensive one)I can record my LP's to CD's
and they can sound just like the LP's do now. I do not want to use my
PC and a bunch of different pieces of equipment. If it's a two piece
matched unit and that's all i will need that's fine to. Help.

I haven't heard of such a unit, the best way to do this (but that is
solely my opinion) is buy a cd recorder  and connect it to the aux
port of your stereo system and play your records on your turntable
whilst recording them (like we used to do with tapes in the good ol
days)

The PC is a good choice, however: AUX out from your record player to
line in on your sound card, then record WAVs, MP3s, etc, then burn to
CD. It is probably cheaper to do this (~$6 for a cable
http://www.radioshack.com/product.asp?catalog%5Fname=CTLG&product%5Fid=42-2550
or http://www.radioshack.com/product.asp?catalog%5Fname=CTLG&product%5Fid=42-2551,
~$35 for CD/R/RW) than a stand-alone CD Recorder
http://froogle.google.com/froogle?q=cd+recorder&btnG=Search+Froogle.