As long as you don't have to worry about stupid cats getting into your tanks like I do, you can pick up a $12 10 gallon tank just about anywhere. Some places might have them cheaper. Toss in some gravel for $5, a heater for $15-18, a lil cave for $5-10 and maybe some fake plants for $5 and you're good.
$12 - 10 gallon tank
$5 - Gravel
$18 - Heater (Got mine from Petco $17.99)
$7 - Cave
- and / or -
$7 - Plants / Rocks / Some kind of hiding place
If you add all that up together, it's about $49.
Might be talking another $3 for betta pellet food.
Edit: A thermometer would help too. Another $1.50.
Also, you could grab a kritter keeper instead of the tank. Same price or a little less, but takes up less space.
Also also, keep in mind with anything smaller than a 10 gallon, you'll be doing very frequent water changes if you want to keep the water in good condition for him.