If you are worried about spending 400 bucks, you will never burn a barrel out. It should be good for 2000 rounds or so. Ammo costs about 1 dollar a shot or more.
A savage barrel can be replaced easily without a gunsmith if it ever burns out too. When you replace it, you can move to any caliber based on 308 by only changing the barrel. That is .243, 260, 7mm 08, and 308
While out of your budget, a close out tikka t3 can be had in the 450 dollar range. That is a lot of gun for the money.
Look at the cost of ammo on cabelas or midway and compare. 243 is significantly cheaper than 25-06, 260, or 6.5 creed. I think 243 is a great starter gun. It will smack any dog as far as you can shoot, and it will drop deer too. If you want a coyote gun that can take a deer go with .243. If you want a deer gun that is not too overkill for coyote a 25-06. .260 may also be great, just consider ammo is harder to find, but they had some at bass pro when I was there last week.
The 25-06 does not really have high BC bullets for long range available, but I would not be worried about it myself. A 24" barrel would also be better for 25-06. That limits gun choices if the length matters to you.
If you are not going to hunt any big game, do not overlook a 22-250.