Sure, 10 gallons would work great. I'd get 1 bag of fluorite as your gravel. There are other options, but fluorite is effective and can be used by itself. I also think it looks nice and it comes in several colors.
Another thing is to make sure your light is sufficient for the plants. When you buy the hood keep in mind the lights you want to use. Incandescent light won't grow anything. The standard fluorescent fixture for 10 gallons is T8 15W. The spectrum of the bulb makes a big difference; you should get "daylight" bulbs or ones specifically designated for growing plants, since they use certain wavelengths of light. You can grow some easy stuff with this. If you want to grow more different kinds of plants, you can invest in fancier lighting.
Get a power filter, it will be cheap. Avoid undergravel filters, apparently they remove nutrients from the substrate and mess with the root systems of the plants.
Now I assume that you have a 10 gallon tank, power filter, fluorite, and fluorescent hood with 15 W bulb. I estimate that all this together will cost around $50 new. Then buy plants: easy plants are Java moss, Java fern, Anubias species, Cryptocoryne wendtii, dwarf sag, anacharis, and hornwort. I'd get a good aquarium plants book from the local library to find out which plants are appropriate.
Then set up the tank, plant it, and add fish slowly. The fluorite will cloud your water at first; wait for it to clear before adding any plants and fish.
If you like, you can make one of those DIY CO2 injectors; personally I think it's quack.
