A belated welcome to the forum. Lots of folks here have a lot of collective wisdom so you're in the right place.
I read your other thread, and would suggest the sulfur-like smell could be your water conditioner. I have read that Prime, a very good wc, does have such a smell. In a new tank I wouldn't expect it to be signs of trouble like dead spots in the substrate, so this is probably it.
Anyway, to your plant questions. Small-grain gravel works better with plants, but you can manage with what you've got since you won't have that many plants in a 3g tank. You have intense light, I'm assuming it is a compact fluorescent bulb? You will have to reduce the light period, which I'll come to momentarily.
Plants require a balance of 17 nutrients, one of which is carbon that they usually take as carbon dioxide (CO2) which comes from the fish respiration and biological processes that occur in any aquarium. There won't be a lot of CO2 with one Betta, so the light will have to be no more than what will balance or other problems will arise like algae. One trick is to stagger the light period with a mid-day siesta. Instead of having the lights on for a straight 10 hours, have them on in the morning for 5 hours, off for 2-3 hours, then on for 5 hours. Arrange the on times for when you are likely to be viewing the tank. A timer from the local hardware store is useful to set the light times.
In the other thread kymmie mentioned a temp of minimum 80F for a Betta, so I would suggest you get a small heater. They have an automatic thermostat that will not turn the heater on unless the temperature falls below the setting, so it may not be on much but that is fine; you don't want to chill the fish. Buy a good one, even though more expensive; the smaller heaters can be poorly made and are frequently the most troublesome, so a good brand is best. You will need to keep the tank well covered to keep the air above the surface most and warm (humid). Betta's are anabantoids, a fish that possesses a labyrinth organ that allows it to "breathe" air and it must do this or it will die.
There are a number of plants that would work in your setup. One certain thing is a floating plant; Betta's like B. splendens are bubble nest builders that live in quiet swamp-like ponds like rice paddies and ditches, thick with floating plants, so it will feel right at home. Ceratopteris works perfectly in such a setting, and will help to shade the light.
For the lower area, rooted plants like crypts (most species are fairly small) or the smaller swords, such as the Pygmy chain sword
or Echinodorus amazonicus would work. Stem plants would grow well, but fast and require regular trimming (weekly), but if that isn't troublesome you could try Wisteria
) or other Hygrophila species.
Some nutrients that the plants require will arrive via the fish food, and maybe a few minerals in the tap water, but usually one has to supplement with fertilizer. Seachem's Flourish Comprehensive Supplement for the Planted Aquarium or the Kent Freshwater Supplement are both good products. Very little will be needed, maybe once a week after the partial water change.
This should get you started; any further questions, ask away.