Sk3lly gave some good advice. Carpeting plants would grow faster and hug the ground (carpeting) better in higher PAR. But higher PAR means more risk and requires better "balancing" between light intensity, duration, co2 (or co2 booster/excel), and ferts. Or else the Algae monster will come out and bite you! haha
A desk lamp with a CFL is cheap and more than adequate to grow DHG and HC (dwarf baby tears). But your limiting factor might be CO2... although the CO2 booster will help. You can always rig up a DIY co2 generator (yeast/sugar). But that would be good for a tank 10-20g, IMO. The 3g you'll risk gassing out any inhabitants.
I haven't used CFL's personally, but I know a guy who grew an amazing high-tech tank with HC and fast-growing stems with 2x CFL's... but his tank is 17g's so it's taller and larger. So 1 CFL would do the trick on a nano tank.
ADA 60P|Glosso carpet| PurpleMonkeyDishwasher
But if you want a nice LED light for that nano tank, you can get a Finnex FugeRay-R clip light.
Amazon.com: Finnex Fugeray-R Ultra Slim Aquarium LED Light Fixture: Pet Supplies
That would grow both DHG and HC if you add a few inches in substrate depth. My personal opinion, I'd also get rid of that gravel and use something more planted tank friendly like Sand or Floramax/Eco Complete.
You need at least 30 PAR (which is the starting of "medium" light) to grow those plants. Your 3g is 14.6 x 8.8 x 11.2 inches. So with the FugeRay-R, if you get the distance from light to substrate to about 10 to 11", you should get about 30 PAR with the FugeRay-R (according to the PAR charts released by Finnex).
Here's another option... cheaper than the Finnex, but a little more expensive than a desklamp. It would work as well.
http://www.amazon.com/Fluval-Mini-P...=8-1&keywords=fluval+compact+fluorescent+lamp