Wow, he's very pretty!
I'd like to note that if you're careful about your water changes, and especially if you find him live plants, he CAN live happily in that tank. But if you'd like to get him something better, there are both efficient/cost-effective and frustrating/expensive ways to go about it.
I suggest getting yourself an ordinary glass tank. PetSmart sells the "Grrreat Choice" brand tanks... they're cheap and basic. Find or make yourself a lid (this can be a piece of fabric tied around the top with a ribbon if no other suitable material presents itself; I plan on making one out of the thick plastic material that tablecloth covers are made out of for mine). He WILL jump out if given the opportunity.
Next, equipment. Get him a heater--5 watts per gallon is generally the minimum unless your house is cold--and make sure you get one that's adjustable. A filter is optional. Get the biggest tank you have space for, because it's not much more expensive, gives him more room, is easier to keep, and is easier to find equipment for. Small-tank heaters are very unreliable. A 5-gallon home is very easy to heat, however, and very easy to maintain.
In ten gallons, you can keep select other fish with him if he's okay with it and if there's plenty of cover. In more than ten gallons, you can get away with a wider variety of tankmates. Something to consider if you like all sorts of fish. You must never keep him with another betta, obviously, or anything that looks too much like one.
When you buy any equipment, especially filters, read reviews first. 90% of everything is crap, especially aquarium equipment, so research first.
Also make sure that any ornaments you buy are aquarium safe BEFORE you put them in. This doesn't mean checking for a label that says "aquarium safe." It means sticking it in a bucket of water conditioner-treated water for a few weeks and then examining it. If anything's bubbling, chipping, flaking, leaching, smelling funny... take it back to the store.
The exception is live plants. Never buy live plants from a store's fish tank, ESPECIALLY if the fish look sick or dead. The ones in the tubes are all right, but still research before you buy; some of the plants sold in tubes are for lizard habitats and aren't fully submersible. They'll rot in your aquarium. Others require special fertilizers or CO2 injection. The ones you want are java/"el nino"/tropica/windelov fern, java moss, water wisteria, floating plants, and marimo moss balls. Those don't require any special fertilizer or anything, just stick them in. They'll help absorb the ammonia produced by your fish, making the tank safer. Sometimes the ferns even come with baby ferns attached under their leaves--bonus!
That's all the advice I can think to give you right now. If you're on a tight budget, I can give you recommendations for that too--but, remember, he will be perfectly happy in that 1g tank as long as you keep it clean and warm.
Welcome to the forum!