remington is an interesting gun... They sometimes fire without the trigger being pulled, causing much surprise, and sometimes startling game that you'd been stalking for hours... Remington has been on a real downhill slide since they were taken over by a financial group. Now, they're all about profit over quality...
Tikka has a real following. I haven't used one myself, but I hear that they're quite good rifles. I have held one, though, and they feel ok to me.
If it was me buying, and I had it to buy my guns over again, almost everything would be CZ. The guns are in about the same price range as the Tikka, but, to me, they have a much nicer feel. I"m a mauser action lover. The cz has made some nice improvements to the action, and for the dollar, have by far the nicest stock trigger of any gun I've handled... Sometimes they have to be adjusted, but they're really nice... The Lux and full stock is better if you like iron sights, and the american is better if you like scopes.