Alrightt, so I'm buying a new rifle! I hunt private land in PA. Our biggest game animal is the elk, but with 60-some tags drawn a year, I doubt I'll be doing a lot of that.....
So I need a rifle that will take mostly whitetail cleanly, but also the occasional black bear. I'm thinking either a .270 Win, 30-30, or .30-06. I have a .308 but it's a 760 Gamemaster from the '60s. I've got the "bug" to get something new and impressive. Ideas?

EDIT: Price is a pretty big issue. Maybe under $800? $900 max.

Remington 700 BDL 270...you can go from 90gr bullet up to 160gr ..that should and will cover just about everything in between.

Is there any particular reason you want to change calibers?

Mace - as another PA hunter you can rest assured that your .308 Gamemaster will take any whitetail cleanly and is also capable of killing an elk cleanly should you be lucky enough to get one of these cherished tags. Some other things you should consider is what else you plan on shooting with your new rifle. Are you going to use it for coyotes, groundhogs? If so, a .243 is good for these critters (a bit more than needed) but I guarantee you that with a 90 - 100 gr bullet, it will drop a deer about as quick as any other medium sized cartridge. That would be my choice if I were going to keep the Gamemaster. I would have to sit and count all the deer I shot with my old Savage .243 and 100 gr Hornady SPs pushed by 40.5 gr of IMR4350.
The most important thing though is if you really have the desire to get another rifle is to be sure it fits you. If you decide on selling the 760 for another rifle go with an '06 and let me know how much you want for the .308.

After my first post, I went to the Winchester Ballistics chart. With a Winchester Power Point bullet, 150 gr. (I know... bullets are a whole new discussion... but I wanted a constant) I compared the 308 with the 270. The results are close.

Sighted in at 50yds with 1 1/2 inch sight height

270
50 yds line of sight 0" - speed 2717 fps - energy 2456
125 yds line of sight 0" - speed 2524 fps - energy 2120

308
50 yds line of sight 0" - speed 2665 fps - energy 2364
125 yds line of sight -0.1" - speed 2444 fps - energy 1987

The next question is recoil. The stronger the "kick" the harder it is to put the next shot on target. I have no experience to comment on either caliber. Note that a semi-auto will absorb kick.

The rifle itself is old and not as accurate as it used to be. Also, the 760 is a pump which I am not a big fan of when it comes to rifles. I'll be looking mostly to a lever, or maybe bolt action.

I love calling in predators, but I already have a .243 as well as a .223. So the new gun should be specifically for deer. I'm not a huge fan of the 760 (still like it though) because it is a pump that I recently acquired from my father. I've never been a huge fan of pump actions on rifles. I prefer a lever or bolt.
I am not looking forward to selling the 760 as it was my father's, and his father's before him. A family thing, you know? For this reason I would like the new rifle to be relatively cheap.

Don't get me wrong... I'm not questioning you wanting a new gun... just asking why you wouldn't buy a new rifle with the same caliber

Well Mace IMO you definately do not need a belted magnum. And you already have a .308. My favorite rifle lately for hunting in here in PA is a nice handling lever action. I have grown fond of these rifles in my old age. I just acquired a Win 94 in 32spl that I plan on using this year. My bear rifle is a Marlin Guide Gun in .45-70. I just love that rifle.
For a bolt action you can't go wrong with the good old 30-06. Another choice if you're looking for a bigger caliber is the 35 whelen (a 30-06 case necked up to .35 caliber). And if you're looking for a smaller caliber I would recommend the 7-08, 270 or .280 being that you already have a .223 and .243.
The number of choices almost seems endless.

If you dont want anouther 308,then dont get one.it sounds like you want something diffrent so get what you want,theres awide range of calibers that will do what you want.Just keep in mind cost and availabilty of ammo and how the gun fits you and go have fun.