In order to have plants you'll first need to get proper lighting and ferts figured out as well as a medium.

Easy low light plants that I kept in my old 20 gal (with a 15 watt Flora max bulb so 0.75 watts per gallon) with a gravel bottom and only the addition of Flourish Comp and Fish include:

Amazon sword

Jungle and Corkscrew Valisneria

Various Anubias

Java Fern

Java Moss

Crypts

And Water wisteria.

The type of plants relies on the amount of light and size of tank so these may not be the best depending on what you plan to set up.

Trying to create a self sustaining fishtank will still require regular maintenance from ferts and adding back water once it evaporates and so on.

Aquatic plants can be found really at any petstore.....Petsmart is a pretty cheap place and usually has a decent selection (stay away from mondo grass, lucky bamboo, and a few others that are sold as aquatics but aren't). There's also a ton of websites to order from. I've never used one myself so I can't really help you with that.

I picked some plants from local rivers and creeks, and got a few more from craigslist or from friends that had extra. Just isolate them for a while to make sure they do not introduce anything unwanted into your aquarium.

I also saw the lucky bamboo at Petsmart and thought, why buy from their expensive prices? I'll get it elsewhere. So I did, and I have it submerged with the leaves popping out of the water line. It grows fairly slowly so I can't tell if it is doing badly or doing well, but the leaves have not turned yellow or squishy yet. But I do know that if it's left out in sun or cold, the leaves die off very fast, so this could mean that it's at least tolerating growing in the water.

My local Petsmart also has some water plants combo for $6. It comes with 5-6 seeds or bulbs. This is my first time trying it. The company says it is guaranteed to grow in 30 days. I'm at day 10 or so, and only 3 bulbs have shown any life, so I still need to wait and see if this is actually a good deal or not.

I also discovered that my Mexican petunia plants are doing OK growing in the aquarium also. They have long stems, and each node could grow roots to help increase the amount of root matter soaking up the nutrients. The stem part is in the water, and the leaves are growing outside of the water.

And finally, I am just now trying pothos ivy. It will hang somewhere on the aquarium, and have its roots growing down into the water. I also have seen some people do a similar thing with spider plants.

You can also buy these plants on places like Ebay. You'll get more bang for your buck but just be careful of sellers, etc.

My list is different from MrBulbs because I was trying to get plants that can live in water or near water, without resorting to the prices for the typical aquarium plants.

If you go with the terrarium idea instead, where it's not as full of water as the aquarium, you could also try some mini-plants that are designed for terrarium landscaping.

all anubias are slow growing plants. i consider cryptocorynes and java fern somewhat slow, too. amazon swords, vals and others mentioned will grow quickly once established.

one of the fastest growing stem plants that comes to mind is anacharis or elodea. these are great oxygenators and also remove a lot of nitrates from your water, keeping it clean. rotala rotundifolia is another good plant.

i will recommend diana walstad as a source of information if you want what she refers to as a "natural planted tank". she used soil as a substrate (miracle grow organic i believe is one brand that is recommended) rather than the various gravels and sands offered at pet stores. her method makes sense to me even though I am pretty much a traditionalist with my methods.

diana walstad's natural planted tank method

good luck with your efforts.

I have great luck with Cyprus Helfer and elodea and also hope you find the right plenty good luck

Srry autocorrect I meant to say Cyperus helferi