For the light you'll want a compact fluorescent around the 6500-6700K range. I get mine from walmart. This will not heat the water. You do not want the light to heat the water as it causes temperature flucuations when you turn it on/off... this constant temperature change can weaken the betta's immune system. For the plants, you'll also want to have the light on for about 10 to 12 hours during they day and then shut it off at night.
This being said you will need a heater. Bettas are tropical and need to be kept at a temperature of around 78 degrees. It can be a little lower, little higher, but the important thing is that it is stable. Don't want to get below 70 to 72 degrees.
Agree with the females. A 5 gallon tank will be perfect for one male or
female betta. A couple shrimp or snail would be great too.
Gravel or sand is a preference thing. I'd google some images and see which you like better, and then your local pet store should have what you need.
Your tank sounds great, but the water must be kept clean or it will affect your betta. You can cycle this tank (if you add a filter). Google the nitrogen cycle
to learn about cycling. It will allow you to make less frequent water changes because of a build up of healthy bacteria. Otherwise, you will need to be doing frequent, substantial water changes throughout the week.
This has kind of been covered, but bettas are lone fish that do not work well with their own kind. Female sororities can be made, but you need at least 4 to spread out the aggression. You can achieve this with a 10 gallon tank or larger. In a 5 gallon you really won't be able to add any other fish, but in a 10 gallon you would be able to add a few select species that tend to do well with bettas. These include platys, cory catfish, shrimp, snails, african dwarf frogs (difficult in their own right), possibly some schooling tetras. However, each betta is different and may not be alright with tank mates.
Another option is to get a 10 gallon tank and divide it so you can have two bettas. You can buy or make dividers that will split the tank right down the middle.