Welcome back. It looks like you're well covered for guns for almost any kind of hunting you want to do. I'm guessing that your "22" is a .22 LR rimfire gun. Since you have to wait a month for your license, you're probably too late for most of the hunting seasons in your state aside from small game, waterfowl and predators. Members will be glad to offer you advice but it would help if you had some idea of what you want to hunt. Most hunters tend to hunt locally in their own state due to cost constraints and sometimes time or vacation limitations, family commitments, etc.
Aside from obtaining your hunting license, you should attend (possibly a mandatory requirement in your state) a Hunter Safety/Education class. Such a class tends to cover safety and laws that you will need to know for your state. It's also a place where you might network some with other hunters and learn more about hunting opportunities in your state. In addition to taking this class, study your state's Game Commission website so you know the laws, seasons, methods of take, etc. There will be some overlap with Hunter Safety. Also, don't hesitate to contact a warden or wildlife biologist to find out about more opportunities. You can also check out local gun shows and hunting shows to find out about more hunting opportunities and meet more people. The same with local gun ranges, hunt clubs, etc. And don't hesitate to do some internet searches.
People are all over the map on what they prefer to hunt. Bear in mind that just about any hunting can end up being expensive. Some guys/gals hunt just waterfowl. Others join pheasant hunting clubs where they buy birds that are released in rice fields, etc. to hunt with a dog. Some people do upland bird hunting like quail, grouse and/or turkeys. Some people hunt varmints like ground squirrels, marmots, etc. Others hunt predators like coyotes, bobcats, fox, etc. Some people hunt big game which can include deer, black bear, elk, moose, grizzlies, brown bears, caribou, etc. Most states have some type of deer hunting and often black bear hunting so you find lots to do in the Fall. In some states, deer seasons can last until December or even January.
Some states allow air guns for hunting turkey and small game. Others do not. Some states require a shotgun or straight wall cartridge for hunting deer, etc. Others do not. Most states have a separate archery season for big game that usually starts before the gun season so you get first crack at the animals. Most people only hunt within their own state. It may sound limiting but it's not. Lots of seasons overlap so you end up triaging your hunting time.
For instance, Mass has a lot of hunting seasons to keep you busy.