Start with budget and requirements. How much do you have to spend and what do you want it to do?
For shotgun, it is hard to go wrong with the good old Maverick 88 in 12 gauge with a fixed Modified barrel. 12 gauge is *a lot* of gun at full honk with 3-inch magnum loads, but target loads aren't too bad for getting used to shooting and despite it being bigger than a 16/20/28 the ammo is far easier to find and cheaper, to a degree. That will take you from popping clays to grouse to turkey to waterfowl no problem. Stepping up a bit in price to a Mossberg or Remington or Benelli pump will get you interchangeable choke tubes and more improvements in build quality, adjustability, and aftermarket support. You need to decide if that is worth the cost.
For rifle, yes, Tikka rifles are awesome. I would absolutely recommend one for hunting. If you fancy deer, ignore the haters and get a 6.5 Creedmoor. Same as with the 12 gauge, it is really popular so there are some good values out there for hunting ammo. If you want to maybe take a pop at a black bear or moose I'd step up to a .308 Winchester, a bit more weight and frontal area with not much more recoil, also with a lot of ammo choices. If the Tikka price tag compromises your optics budget, I would look at a Savage 110 or Ruger American. Step down in build quality and fit and finish (reflected in the price tag) but they are safe and generally quite accurate.
New or used for the above is fine as those models are all in wide distribution with factory support and warranty available. Old used guns are neat and all, but you lose a support network and reliable parts supply. An example, I have a Savage 110 that arrived with a cracked trigger guard/bolt release. I opened a ticket on their website, got an email a day later from their support guy confirming my info and problem, and had a replacement in my mailbox in a few days.
You should also budget for a scope and a mounting system. Some guns include bases but you still need rings, and often the included bases aren't exactly the best quality. Most of the scope manufacturers with decent scope offerings in the lower range offer good mounts in the lower range as well, Vortex, Leupold, and Burris specifically. Talley and Warne make great stuff too. For scopes themselves, buy the best you can. Vortex Viper, Leupold VX-Freedom, and Burris Fullfield IV are all fine scopes with good warranty support that I would bet my hunt on without breaking the bank.
You also need a rimfire, period. That goes without saying around these parts, volume of fire is important for reinforcing good habits. I have no real preference here. Ruger 10/22 is a solid choice and a lot of fun. I've also got a Savage 93 bolt gun which is a lot of fun to shoot. I've owned a bunch of used guns, Cooey and related model are a staple in Canadian gun safes. I would probably stay away from "tacti-cool" guns for your first one. And you can scope it with pretty much anything, although you will appreciate decent glass with adjustable diopter if you plan to shoot a lot.
