If it were me, I would shoulder all of them, try out the trigger if you can, see which one you like. I'm not about to start bashing another brand. I like most all guns that go boom, so I don't have much bias. There are a couple of things to consider.

The Ruger rifles require you to use their rings on all of their rifles. The rings are decent, but you won't have the ability to change the location of your scope, not like you can on an AR-15
I have no personal experience on the Tikka, so I won't comment on them, same goes with they weatherby.
The Remington 700 is an awesome platform. Arguing between the Savage vs. Remington is like arguing between Chevy vs Ford. If you plan on leaving your gun the same, ie not changing your stock, trigger, barrel, either one will serve you fine.

The biggest advantage to me that Savage has over Remington, is that Savage typically offers more variety of land handed rifles. If that weren't an issue, then either one will server you fine. Honestly, you'll be best serveed spending the most money can on the glass. Buy once cry once. Find a rifle that fits your needs.