I'd go for the Philips 5960 which you can get from Evesham for £35 delivered.
http://www.evesham.com/products/info.asp?e=086FDDBE-6BC0-4460-9CAA-7B65183D9232
By AVI I assume you obviously refer to the mpeg4 /divx/xvid/mjpeg type files.
Its easy enough to burn them to a cheap 10-20p DVD though, and most DVD players wont have a problem with playback as long as the codec isnt non standard
Similarly , many CD players ( and most DVD players) can play mp3s burnt to Cd as a data CD
My TV (Phillips Cineos series) has a USB slot and can play some ( not all) mpeg4 files