You can play REUC, everything in it happened before RE4.
If you have a Wii, i reccomend you to play RE The Darkside Chronicles after REUC. REUC and RETDC are a resume of all the RE's before RE4.
The chronological order of the RE games is: RE0, 1, 2, 3, Code:Veronica, 4 and 5.
REUC is a resume of RE0, 1, 3 and has a new chapter and RETDC is a resume of RE2, CV and also has a new chapter.
Leon from RE4 was also in RE2. That's when he meets Ada (also in RE4). Ada has a "secret" chapter in REUC.
After that, you'll only have to play RE5 (don't play RE5 before REUC)