I would not get the under gravel filter. The reasons being that 1) they have fallen out of favor with a large majority of the aquarium community, 2) they won't really help reduce your bio-load in a 2 gallon tank, 3) the bubbles and agitated surface they create will make it difficult if not impossible for your betta to create a bubble nest. Of course you can always get a tank with an under gravel filter and just not use it, but I would avoid paying extra for one.
And just to clarify what I said earlier, I recommend a desk lamp only for light for growing plants, not to heat the tank. Though CFL do get warm, they should not be close enough to the tank to make a significant change in temperature.