First step up from what you have is a good brush gun, and considering your location, it is hard to beat a .30-30 lever. It is undoubtedly the most popular in history. Great varmint gun, good for deer up into the 100 yard range. I prefer a .45/70 lever, but here in the Rockies, a little more poop is nice because of big bear and moose, etc.
Next would be a long range rifle - Like many here, I would recommend a Remington 700: 30-06 is fine, as many have recommended... I shot a 7mm Mag for years, and now have a 300 win Mag, which I will stay in till I die...
But a good brush/saddle gun is more important. Scoped rifles are good for their purpose, but that purpose is 125+ yds. They generally suck in the woods, where it is uncommon to get a range of more than 100 yards, and often down to 50yds, where a scoped rifle is just about useless, and high power will cause deflection...
Ask BATF which ones they hate the most and there is your answer.
I've done cast bullets down to 80gr for rabbit loads, had to work out my own loads, and that was decades ago. Bolt-gun only. Autoloaders are a lot more finicky about ammo.
Not done much shooting in decades, so there are lots of new toys to try, and new powders to play with that I haven't used. And lots of good info on this thread. Have fun finding your next gun!
Since your budget is a bit more restricted, you may want to cast about for a Gibbs #7 Jungle carbine. It would have to be used, but it get's you a short bolt action rifle in 7.62x51, and I've seen them at very good prices through a number of online auction houses.
Many good suggestions.
Here are my 2 New Jersey utilitarian suggestions if you choose to continue to reside there.
Com Bloc standard - CZ527 in 7.62x39. Bolt action, mid-grade, carbine. - Add passable glass, and you’re at the top end of your $900 budget.
NATO standard - Stevens 200 in .308 Win. With a $900 dollar budget, you should have about $600 to spend on glass after the purchase.
Both are accurate, rugged bolt-action rifles. The CZ is much nicer in terms of finish, but the Stevens can be customized as money permits. Stocks, barrels, triggers, etc. are all readily available for the Stevens and it’s no slouch in the accuracy department right out of the box.
As for glass...Swarovski, and Schmidt and Bender are not going to happen on this budget. However, there are some nice Leupold, Bushnell, Nikon, and Burris glass that will get the job done.
Looking over that list...New Jersey really does limit how one expresses their 2nd Amendment freedom.
Regardless of what you choose, good luck on your purchase!
(And, this information is worth exactly what you paid for it.)
30.06 bolt-action. Savage makes a pretty good and economical model 115 (I think). Ammo is common, muzzle energy is very good and it’s a very proven round.
Bolt Action:
Remington 700 in .308. Good, all-purpose round, solid, proven design.
Lever:
Winchester .30-30. Ubiquitous. Simplistic. Effective, especially at closer ranges. Proven design.
Automatic:
Saiga .308. Made like a tank, based on a proven design.
Kel-Tec SU-16 .223. Several variants to fit your needs (and New Jersey’s inane laws). Compatible with AR-15 mags and ammo. Lots of aftermarket parts. Not a proven design, but loosely based on an AR, but piston driven instead of gas. I’ve seen one torture tested, and it held up beautifully.
Single shot:
Rossi Trifecta - .243, 20 gauge and .22 long rifle out of one gun via interchangeable barrels.
In theory, you should be able to get anything here for under $700, if you look around and select the right variant.
Have fun.
Of course, everyone know you need a minimum of 6 weapons to have a full spectrum:)
I can only suggest that you move first, and then think about what you will need the rifle for.
Since I live in Alaska and game is plentiful I will make my suggestions based upon a general safe caliber and type of rifle.
First off it should be weather protected either by any of the recent new coatings or all stainless steel.
Second it needs to be legal to use on most game and of sufficient power either close or long range, so then I would say get a Ruger 77 Mk2 in stainless, I have one, its a controlled fed round which means you can chamber it upside down. Its a bolt action, the original composite stock was ugly and a pain to shoot, I replaced mine with a Hogue rubber coated fiberglass stock.
Next is the caliber, the majority of professional guides up here swear by the .338win, its heavy enough for bear and between the different weights of bullets stays pretty much the same ballistics. But it isn’t a plinker and is an overkill on small game, but it will do the job on anything else.
The lightest caliber I would use is the .270, its taken down African game in many a hunt but is a poor choice for dangerous game in the brush.
With some modest gunsmithing a muzzle brake and a sorbothane recoil pad will tame the recoil of the .338.
The other most popular cartridge is the .300 and 7mm.
What would I carry if I had only one choice? It would be my M1A in .308 with Barnes bullets. Or a Garand in 30-06 a caliber that has the most options for bullet weights.
For the lower 48 that is a good caliber, and a decent Garand with a good barrel will bring home vittles.
But buying either the M1A or a Garand will cost some serious money. I have a Mini 14, and an SKS and both were pretty cheap, neither is terribly accurate though. For affordable accuracy its the bolt action. And a good scope.
Rule of thumb, the scope will cost just as much if not more than the rifle, never scrimp on the scope and the mounts.
Great for Jersey Turnpike traffic jams.