Specific recommendations based on guns I've shot/owned:

Rifles:
Marlin 22 lr https://www.marlinfirearms.com/rimfire/xt-series/model-xt-22

Ruger pc9 (9mm carbine)
https://ruger.com/products/pcCarbine/models.html

Savage axis 2 - 308 win
https://www.savagearms.com/content?p=firearms&a=product_summary&s=57093

AR15: ruger 556 or a for a cheaper ome palmetto state armory or diamond back (decent cheaper one) I would get a 556 chambered one as it can fire .223 or 556 (.223 is the civilian round, 5.56 is the "military round", performance wise theres negligible difference between the 2 but the 5.56 makes more pressure and a gun made for 223 cannot safely shoot it, the benefit is you can buy 223 or 556 which makes it more flexible)
https://www.ruger.com/products/ar556/models.html

Pistols:
Smith and wesson m&p shield 9mm great first pistol. Reliable, accurate (enough) and used by a lot of law enforcement friends of mine. https://www.smith-wesson.com/firearms/mp-9-shield-0

Sig p365 is literally the best pistol I've ever shot in my life, a lot of money, but literally insane accuracy.
https://www.sigsauer.com/products/firearms/pistols/p365/

I'm not at all a glock guy, which pisses a lot of gun guys off, but I do not like them. I hate that they don't have a safety, yes I know the trigger has a built in safety where if you don't intentionally pull it, it wont fire but I've seen too many accidental discharges during my time in the ER to want one. I also think they feel cheap as fuck. But a lot of my cop and military buddies hate on me.

If I had to pick 2 guns to have for the rest of my life, the ruger pc9 carbine and the sig p365 without a doubt. I love my AR and my other guns but the ruger has a button where the barrel comes off and it fits in a back pack or in my case a bug out bag. The sig shoots the same 9mm, I bring all the same ammo with me and I'm ready to rock. Next would be the 308 if I got a 3rd so I can do bigger game hunting.

I don't, I'm up north unfortunately but I do know I bought guns in VA where my med school was with my NY ID and was fine. Any rifle off the shelf is good to go

So it looks like you don't need a permit for a side arm there either, idk if you were looking for a rifle or a side arm but looks like you're fine. If they want you to, you can go to a court house and get a formed signed to let you buy one. A lot of people do that in PA to buy pistols being NY residents. https://www.nraila.org/gun-laws/state-gun-laws/missouri/

I'd recommend a rifle as first firearm, specifically I would go for a .22 lr, they don't have a lot of stopping power but to learn gun safety and shooting techniques and practice, they're your best bet. You can buy a bolt action for less than $100 and you can get 500 rounds for literally next to nothing. Go shoot it as much as you can, get good with it then upgrade to either something like a 9mm carbine (about 500 bucks) but 9mm is still cheap to shoot or a .223 like an AR15 (can be had around 50p bucks) or ruger mini ranch 14 (about 800 if you dont want an ar15 shoots the same load). Side arms are harder to be accurate with, but if you do decide on one - again I'd go 9mm. Stopping power is comparable to a 40 which used to be the standard for law enforcement, but changed to 9mm due to less kick and better accuracy. 9mm is ubiquitous and you can find it from Walmart to you local bait and tackle. If you want something with more stopping power 308 win or 30-06 is my go to. More expensive 15 bucks for 20 but again they're able to be had literally anywhere. When I purchase a gun, I look for the round that will meet my needs and is also available enough that if shit hit the fan I can get it anywhere. Newer rounds like the 6.5mm creedmotor or russian rounds like 7.62 are good and available for the most part at big places but if you're out hunting and low on ammo you may not be able to buy or borrow some.