Hi! Welcome to the site and Happy New Year! Congrats on deciding to keep your betta. He's a beauty and they can be lots of fun. I too am new to the betta world. I just got my betta on christmas eve. I bought a 1gal tank w/filter trusting the info the pet store gave me and ended up back in the store a few days later, after doing my research, to buy everything else he needed that the pet store ppl failed to tell me. I don't know much about betta illness yet but I can help out as far as tanks and stuff :)
I upgraded my guy, Leonard a VT, to a 5.5 gal tank with a filter and 50W heater by aqueaon.
I think most tanks are glass. I would recommend buying a kit. You need a lid for your tank and buying it separately the lid will cost almost as much as the tank if you buy the hood w/light.
This is what I purchased http://www.petsmart.com/product/inde...AvailInUS%2FNo
along with this heater http://www.petsmart.com/product/inde...AvailInUS%2FNo
From what I have read 2.5 gal is the minimum. I think the general saying here is Bigger is better. If 5 gal is too big for you, you could always go with a 3.5g and then you would only need a 25w heater.
As far as plants...some ppl do live plants. Me personally I'm not ready to try that yet so I got silk plants. My guy loves them and they're soft so they don't cut his fins.
At the end of it all it comes down to personal preference and what works best for your budget. Good luck !