$600 total is not a lot for a new rifle.
I would look in the used rack at the local shop for a rifle with scope already mounted.
If you already have optics, I would look at the Howa rifles. Optics are going to be a problem too depending on what and how you hunt.
Weatherby has a 399.00 Howa rifle, the Vanguard. on sale.
As to caliber. I like 308. I think it is a more versital round and is available in at least two weights and or bullet designs at most every shop, but 243, 250 savage, 257 roberts,25-06, 260 rem, 6.5X55 Sede, 270 win, 7-08, 7X57,284, 280, 300 Savage, 308 win, 30-06, 7.62X39, 338 fed, 338-06 all will do the job for deer. Not to mention all of the new designs, wildcats, rimmed, or belted options inbetween these standard rounds. But deer can mean a lot from the Coues deer of the south west to big mule deer in open spaces or whitetail in deep thick woods where a 40 yards shot would be hard to see. Are you going to be stand hunting, still hunting, or spot and stalk? For stand the rifle weight does not matter too much. For the other two a 7-8 pound rifle is about max of what you want to carry in your arms all day. If you road hunt, who cares what the rifle weighs as it will be in the truck.
As far as shooting Varmints, that too can mean a lot. Are you talking a prarrie dog town, wood chuck, or coyote?
And generally a varmint rifle is heavy to absorb recoil.
I say get the rifle for what you are going to do most. and make it do for the other till you can get another rifle for that task.
Heck a 17 HMR out of a Marlin 917V would make do for a 150 yard Varmint rifle till you get what you want.
