Either of these will be OK for varmints up to the size of wolves, and will do for deer also. BUT I definitely would not recommend a .22/250 for moose or bear! The .25/06 will certainly kill moose and bear, but the .270 Win. with 150-grain Nosler Partition bullets would be better for these two!! If your limitation is based on bullet diameter rather than cartridge case size, then get a .270 Weatherby Magnum! A used Weatherby should be available within your price range.

As for accuracy and reasonable price, look at a Savage! They have an excellent rep. for accuracy, and cost less than Rem, Win, Ruger, etc. However, don't rule out a good used gun!!