I have about a half dozen .30-30's. Besides 7.62x39, it's my main caliber. You know what that rifle does.
Get the 22lr next. Marlin 60 or anything bolt action from marlin are great rifles. I have several marlin 22lr bolt action rifles. All of them make quarter sized groups at 50 yards. They go for about $175-250 range.
If you really like the .30-30 and are comfortable with the range capabilities, then stick with it. In NY, rarely does a deer present itself in a situation beyond 200 yards, especially during rifle season.
A decent step up would be an SKS or a saiga rifle. the saiga can be had for about $350 new. When you get some more money save up, it can be converted to a regular AK-47 for about $100-150 more. Very affordable to shoot and own. another alternative is a 12 or 20 gauge shotgun. Quick repeat shot, aim is a bit forgiving with buckshot, and a very effective and powerful ammunition.
In all reality, conforntations will be close. Well with-in pistol range. The next best step in the context of this website would be a handgun of some sort. 9mm or 38 special can be affordable to own and shoot. 22lr pistol would be nice, but I would focus on something with some power. 44 magnum or other heavy shooting calibers aren't good to learn with. Bad habits come in quick.
The best bet is to stay low as possible. Food, water, and seclusion offer much better safety than anything you'll find in a gun shop.