Growing aquarium plants and learning to aquascape is a really fun and challenging hobby. It's a good mix between biology, chemistry and art. Plenty of geeky stuff to dive into if you want and lots and lots of things you'll only learn through experimenting and the payoff is having a beautiful, peaceful nature scene in your home or office that can relax you no matter what might be on your mind at the time.
Contrary to the way it is in most cases with most things, starting out smaller is not a good idea with aquariums. I would also recommend a 10 gallon and here's why:
I have 2 equal shot glasses full of poison. I'm going to take one shot glass and pour it's contents into a 5 gallon bucket of water. I'm going to take the other shot glass and pour it's contents into a swimming pool. Now, you HAVE to drink a glass full of water from one of these two sources. Which one would you pick? You'd pick the swimming pool, of course, because the poison would be diluted a lot more and you'd be less likely to get sick or die.
Same thing goes for fish swimming/breathing/eating in an aquarium. The more water, the more stable the system. The less often you need to change water. The more stable the temperature. The more fish you can keep without causing problems. In a nano, it doesn't take much at all to throw things out of balance and cause problems. I often hear of nanos being considered for advanced or experienced aquarists. This really shows itself when you look at dosing nano tanks. For example, there is a product that recommends 5 ml dosage for every 50 gallons. 5ml is the fill line on most test kit vials. Well, in my 1 gallon nano, that same dosage rate would be .1ml, which is like 3 drops out of a medicine dropper. So you can see how a small little nothing that would make no difference in a larger tank can cause a huge change in a little nano.
A 10 gallon costs 8-10 bucks and depending on the filter you found, you may be able to use the filter with a 10 gallon.
You can of course start with a nano tank. I wouldn't necessarily call a nano a REAL planted tank. They are usually more of a compromise with things and a stimulating challenge to pull off successfully. It is possible that you will pull it off with no problems. However, I'd hate to see you end up with problem after problem and get discouraged by stacking the deck against yourself.
What are your goals? Do you want schooling fish or just a few small shrimp? Water changes every 3-7 days or water changes every 2 weeks? Room to try new plants as you get them or are you ready to limit yourself to 2-3 small species that will fit a nano?
"Insanity: doing [or asking] the same thing over and over again and expecting different results."