Yay a 10 gallon is awesome! I've never had a problem with plastic plants. As long as they pass the "panty hose test". Run some panty hose over the plastic plants and if the hose isn't ripped the plant is safe for a betta's fins.
Glad I could help :) I would say get a larger critter keeper or an actual tank. Any tank over 2.5 gallons is great. I know Mini-Bows are very popular, I like the 5 gallon from walmart. It's about $25-30 with glass tank, hood, light, and filter. You definitely need a heater as well. As for plants, I only use plastic plants since they're easier, but live plants look very nice. If there's anything else I can help you with let me know. Good luck with your future tank!
Well, it really is best to have a heater. If temperatures cchange a few degrees back and forth often, it may bother your fish. Bettas are really at there best when the temperature is 76 degrees or above.
I do think a heater is important, but it's your decision.