Most of the side games are irrelevant. Operation Raccoon City is non-canon, Dead Aim, Survivor, and Revelations are stand alone. Outbreak is stand alone but pointless now that online capabilities are gone. Umbrella Chronicles and Darkside Chronicles on the other hand are definitely relevant to the story.
If you have a 360 or PS3, Code Veronica and RE4 are available for download in HD. PS3 has both Chronicles games in HD, but not as fun unless you have Move.
Just in case you want to play in order, here's a list of the games' story chronologically:
1998- (July 23/24) Resident Evil 0
1998- (July 24/25) Resident Evil
1998- (September 29/30) Resident Evil 2
1998- (September 28/October 1) Resident Evil 3: Nemesis
1998- (November) Resident Evil: Survivor
1998- (December 27-29) Resident Evil CODE: Veronica
2002- (Summer) Resident Evil: Darkside Chronicles (Operation Javier)
2002- (September) Resident Evil: Dead Aim
2003- (February 18) Resident Evil: Umbrella Chronicles (Umbrella's End, Dark Legacy)
2004- (Autumn) Resident Evil 4
2005- Resident Evil: Revelations
2005- (November) Resident Evil: Degeneration
2006- (November 29) Resident Evil 5: Gold Edition (Lost in Nightmares)
2009- (March) Resident Evil 5
2013- Resident Evil 6