Firstly, I'd highly recommend you read the betta care guide that's stickied on the front page of this sub. It's super helpful, and it was my best friend when I was getting serious about owning a betta. I would link the post, but alas, I am on moblie.
As for the breed of betta, pick whichever you like! There's so many kinds! My boy, King Poseidon, is a crowntail. There's also veil tail (the most common kind you see in pet stores), double tail, delta/super delta tail, halfmoon, and plakat. If you want a good, healthy fish, I'd highly suggest a website called Aquabids. There's breeders from all over the world on there, and all the fish are gorgeous! I'd say the average betta on there goes for $15-$30 plus shipping costs. The price heavily depends on the breed and coloration. I hope you find a great fish!
As for setup... If you don't want anything too crazy, the standard for bettas is a 5 gallon tank with a filter and a heater. This is my setup! Marineland 5g tank that came with a tetra 3i whisper filter. It also has a 7.5 watt heater (soon to be upgraded!), and a tetra whisper air pump. I live in northern Pennsylvania so I understand your cold weather problems! The tank's heater will be your betta's bff! Bettas are tropical fish and like warm water between 76-82 degrees F. As for the filter, make sure the setting is as low as it can go because bettas aren't too fond of currents in their homes! For decor, no plastic or sharp edged plants! They'll hurt your betta's fins. If you need fake plants, make sure that they're made of silk. As for logs and such, if you run them against a nylon shirt and it catches on the fabric, then it'll hurt your fish. Both the log and rock in my tank are ceramic and fairly smooth. Sometimes it's easiest to order decor online, to be honest!
As for water changes, I do a 25%-50% change about every four days or so. I check the water parameters every other day. Hopefully someone else might have more insight as to whether or not shrimp and snails help with that as I've never owned either. My betta is all by his lonesome!
I hope this wasn't too long or overwhelming! Maybe this will help at least a little bit. Good luck with everything! :)
