Any of the three calibers would be good. As for recoil it depends on a lot of factors from weight of the rifle, if it has a decent recoil pad, shooting with a sling, bolt or semi/gas operated, etc. Generally the .30-06 will have the most of the three you mentioned, but hot heavy loads in light rifles of the other two may not make that so.
The .30-06 is a fine caliber for just about all North American big game here in the lower 48.
A good recoil pad and a longer eye relief scope like a Leupold can help make rough recoil tolerable. Muzzle braking can also be done but that gets into more money.
I shoot a Remington 700 ADL in .30-06 w/ 24" standard barrel and factory trigger taken down to 3" and a cheap Tasco 3-9x40 scope. Last weekend I shot a 100 yard grouping about 1/2 to 3/4" in size shooting factory Winchester soft point loads. The scope needs to go though since it was having POI adjustment issues.
At the price point you are at I'd recommend looking at the Remington 700ADL, the 710, or a Savage Rifle. I got my 700ADL new with the scope for $409. The 710s are going for around $370 w/ a scope, and the Savages about the same I think.
Use the factory scope to get you started. Plan however on getting a good scope and save the pennies for it. I like Leupold, others have their favorites as well, but a quality scope will run a couple hundred for a basic 3x9.
Realistically the scope is where you want to spend the money. I'm sure the Remington 710s shoot just fine. One very nice feature of the 710s is that they have a 60 degree bolt rotation instead of a 90 degree which gives much more clearance between bolt handle and scope. One downside is that the barrels of the 710s are pressed and not screwed in so there isn't much to do for changing the barrel, but if you are simply looking for a basic big game rifle and occasional weekend shooting you shouldn't need to change barrels in your lifetime. People say it's an ugly rifle, big deal. Deer can't tell if they got shot by a nicely laquered walnut stocked Browning Grade II or a grey synthetic 710 from Wal-Mart. Besides, just camo the rifle up with a couple cans of Krylon and all is well. IIRC the 710 has a Monte Carlo stock which is nice--at least to me.
Savage makes good rifles from the folks I've been talking to. They are like the 710s, somewhat. They may not be the prettiest girl at the party but they shoot well. And my one experience with their customer support was excellent.
Glenn