I have the standard lights on my 10 gallon tanks, 15 watt flourescent grow lights. My plants do ok but they thrive now that I add leaf zone. If you have the room or a way, put a second light behind the tank, another 20 watt. I have a 20 watt behind my 2 10 gallon tanks and the plants do really well. I think the extra light might the reason I have problems with blue/green water but it also gives me more than 2 watts per gallon which is way too much for 10 gallon tanks. A second 20 watt would give you just over 1.5 watts which should be fine for your tank. Assuming you have low light plants.
The key could be what type of plants? They could be high light plants and would require a much higher wattage and
CO2 injection. I have anacharis and java moss in mine and they do fine with the lighting I have.
How many fish do you have in the tank? What kind of filter? An undergravel is death to plants, I know because I removed mine and my plants are finally thriving. If you use gravel, get the finer, uncoated natural gravel. The plants stay put in it much better. Also, don't be afraid to have a good 3 inches of gravel. It not only helps with keeping the plants in place but also holds nutrients better.
I am sure if I am off base here someone will let both of us know.
Don't give up, there are many in the forums that know a lot more than I do and that is where I got all my information. Someone will be able to help you succeed with live plants.
Check out the section on planted tanks and find out what your plants are and what their light requirements are. Is the first step but is probably the biggest one. The getting started part will point you in the right direction.