He will need AT LEAST a 2 gallon bowl. But if you want to go with a filtered, lighted tank an eclipse 2 or a minibow 2.5 are great choices. They are very compact but still a good size for your betta.
If you just get a bowl you will need to do at least 2 water changes a week. One should be at least 20% and the other a full 100% so you can clean the gravel.
Either way you will need a heater. The Hydor Mini 7.5 Watt
heater is a great choice for small tanks IMO.
Other things you will need are:
Silk plants.... plastic ones can tear fins so I would be VERY careful when looking at them and make sure there are no sharp edges.. your fish likes lots of hiding spots
gravel.... for a first timer this is usually the easiest substrate to deal with
A cave... this can be either a terra cotta pot or a resin cave from the petstore
Food... top fin, hikari bio- gold, aqueon are all great brands of pellet... freeze dried blood worms and brine shrimp as a treat
water conditioner... prime is the best IMO but any will work