First Resident Evil game I played was Resident Evil 4, but I've played the rest afterward and it's my favourite franchise at the moment.
Resident Evil 6, now released (got it early since I got it from EB Games Australia), is probably one of the best Resident Evil games, this has given the franchise a lift up.
Although, I haven't fully completed it, I've played enough to tell you what my opinions are over this and hopefully this'll help you.
First off, the beginning of the game.
It's a turtorial, so it helps with the controls, which is really useful, 'cause you're going to need it.
Now a really nice thing you can do is, once you reach the main menu you can choose which ever campaign you want to do first.
I'm not going to spoil it for you, but I had my mouth open almost through the whole game, it's very action packed, but there'll also be parts which will make you panic or frighten you. I was basically freaking throughout all of Leon's campaign.
I strongly recommend getting this game, it is one of the best!