The bigger the tank the better for the betta, and easier for the owner. But a 3g filtered aquarium will suit it fine.
Most small tank heaters, like the ones for bettas, don't turn on/off, they stay on and may have a safety feature if it goes to hot it breaks. The
15-Watt Aquatop Nano Aquarium Heater doesn't. I have use it in a 3.5 and a 5g.
But anyways. If I where you I'd get something about like
this tank, some decor like a cave like thing and get some low light live plants like a "crypt" will do well. I highly suggest having low light plants, it wont rip the betas long soft fins, and helps prevent algae, giving you a healthier prettier tank. I'd also get some tank media or purchase active live bacteria like
Tetra safe start or
Seachem Stability to get your tank going.
Random dump of info:
+Betta's can jump, you want a lid.
+Betta's don't like each other, and don't always play nice with others. Solo is easiest(snail is ok)
+Please dechlorinate the water before adding to tank.
+Betta's don't like current, you may need to play with the filter/adjust flow.
+When tank light is on but the room is dark, the Beta may get aggressive with it's reflection. If thats the case be sure to turn the light off when things get dark.
+Bettas don't each much, 1-2 pellets per feeding 1-2 times a day!(I've seen
many kids kill bettas with over feeding) Maybe be in charge of the food, having your kid what to feed it.(hold old is kid?)
+You may have problems with blue-green algae with a small tank and low current(this type of algae comes of much easier than real algae) nothing will eat it, will just have to do clean the tank and look to remedy the situation.
+You will also need a way to clean the tank,
syphon,
scrubbers, doing partial water change once a month(again, using a
dechlorinator or let it sit for 24hrs) This isn't just about making it look clean, or keeping it topped off.
+
Aquarium test kits are nice. but if I where you. with a single Betta in a 5+ gallon tank I'd skip it.
+If you want an algae eater of some kind, like a snail, wait a few months when you have algae growing(not blue-green algae) and even then you may need special food to keep them alive.
I linked to amazon as examples. I suggest buying all this at your local stores, even walmart has most of this. The hardest thing would be the live plant "crypt" you may have to goto an actual fish store.