OK, We have heard about the .270, .30-06 and big Bell scopes before. I would suggest you check out the used racks. Since hunting season is ending there are lots of great deals on lightly used hunting rifles. Many are purchased, fired at the range a few times and never see the field. You can get a complete rifle and scope for under $600.00, but don't be stuck on any particular caliber. I'm not a fan of big bell scopes either. VG glass w/ a 42mm objective is more than you'll ever need. For 300 and below I use a strait 4x32mm on a 6.5x55. Even my 7mm Rem Mag wears a 2-10x38mm. No need to carry something that can get hung up in the woods. It is really important that a scope has the ability for close shots as most whitetail are harvested under 75 yards.
Now just to clarify, I have nothing against the .30-06 or .270, they are just not my cup of tea. Instead of a .30-06 I use an 8x57, its' Father. Instead of the .270, I use a 6.5x55.
One thing you often hear is that you need a heavy bullet for woods. A complete myth. A .257 Roberts would be a great cartridge for the OP's needs. He could hunt from varmints to Black bear. The .25-06 has a little more punch then the Roberts and I think is more versitile than the .270. JMHO, not a flame. Both use the .30-06 case as their parent. .257 Roberts is a great cartridge overall. Very similar to the 6.5x55 in many respects. It is based on the 7x57 w/ a 20 degree shoulder. W/ a 117 SST it is capible of shoots within 400 yards for whitetail w/ a qaulity bullet. The .243 is a good choice also. My favorite is the 6.5x55. The 129gr Hornady SST is hard to beat. Even a 129 or 139..140gr sp will do the job nicely.
For 100 yards or less I still prefer open sights. My 1943 M46b Husqvarna in 9.3x57 w/ a 285gr cast lead or 286gr partition is a thumper. No real felt recoil, and enough enegy to drop a grizzly at 100 yards. It is cheap to reload for and very accurate, smooth as glass. I also have been useing a Model 92 clone in .44-40. Great 100 yard rifle w/ 205gr soft points. There are so many options out there it is like going to Baskins and Robbins, don't get vanilla.
OK, for my Model 1600 Husqvarna in 6.5x55, I paid 360.00, 1943 Husqvarna in 9.3x57, 320.00.
Marlin makes a VG rifle as does Savage. My Savage 110 in 7mm Rem Mag looks like a 2x4, but when you shoulder it and shoot it it is awesome. I know where a g series 110 is in 7 MM rem mag is that is still new. Needs a front sight blade as they were shipped without them. $3.99 from Brownells. $275.00 + shipping. My suggestion is look around and handle a few. How a rifle shoulders is more important then caliber and trigger. JMHO