In order of release (1 2 3 CVX Remake 0 4 5 6 Rev Rev2), definitely. Remake can be substituted for original RE1 if you don't feel like going through roughly the same game twice - they're not that comparable though, Remake is streets ahead of original ports of RE1. They're both worth playing though.
The only ones I'd skip are the Outbreaks. With their online services shut down, it's impossible to get the best ending since certain endings are only available with character combinations you could only find online. That, and their continuity is heavily debated.
The first Gun Survivor though gets a shout out in the beginning of 0. The Chronicles games are a mix of quick retellings of the games to get folks caught up and original stories which generally cover scenarios hinted at, or behind the scenes, but never expressly shown. For (spoiler free) instance, a new character in RE4 is revealed to have a past with someone, but that's his first appearance in the series. One of the Chronicles games has a scenario that goes into their history in greater detail, but there's also missions that are just basic recaps of other games in the main series.
The best platform depends on which game we're talking about. The best version of the first one is the PC version, due to its superior graphics and extra features. The Saturn version has additional features on top of that, but the graphics are considered the worst for its time. If you have a DS, the DS port of RE1 is good, with puzzles and features that make good use of the touchscreen and microphone. The graphics are somewhat washed out due to compression, but it's good enough for the ds.
For RE2 and 3, the best version for both is either the Dreamcast version or the SourceNext PC port, due to graphics and content.
Code: Veronica had an expanded port in the early 2000s known as Code: Veronica X with new plot elements and features. Recently, CVX (as well as RE4) was given an HD port to the PSN/XBLA.
RE4 was then ported to Steam and given a greater overhaul in terms of graphics, featuring new textures, GameCube lighting/effects, and running at 60 fps.
Remake was just given the same treatment, with a Steam port similar to RE4's. 0 is supposedly next for that same treatment as well.
RE5, either the PS3 or the PC version. PS3's Gold Edition comes with all the DLC on disc, but the PC version has an exclusive mode for Mercenaries, Nvidia 3D, and is about to be updated with the DLC from the consoles.
RE6 is, again, the PC version, again due to it's exclusive content for Mercenaries mode.
Revelations, any of the HD ports should all be equal, though the PC version obviously supports anti-aliasing, higher frame rates and resolutions.
Rev2, the console releases are likely the best right now, as the PC release had its coop gutted just before release. They're working on patching it back in, as far as I know.
As for side games, RE: Survivor/Gun Survivor, the best version is the European PS1 version, as the US version cut guncon support. Gun Survivor 2 was only released in Europe, Survivor 3 was about Dino Crisis, and 4 was released as Dead Aim in the US. It's pretty fun, combining the over the shoulder controls of RE4 with the exploration of RE1. It switches from it's third person camera to first person controls when aiming the light gun. Overall the Survivor games are skippable, but the first one gets a shout out in RE0 making at least that one canon.
RE: Gaiden is completely skippable unless you like quirky RPGs and absolutely love Barry and Leon.
That should cover everything other than don't bother with Operation Racoon City, and check out the CGI movies, Degeneration and Damnation.