For a cheap, attractive small setup, here's what I'd get:
First, an all-glass Cube Flower Vase:
These things are sturdy, easy to find, and more importantly--
much prettier than your standard aquariums with those
ugly black rims. :S
Next, a mini HOB (hand on back) Filter, something like:
http://www.petco.com/product/12148/Red-Sea-Deco-Art-Nano-Filter.aspx
Red Sea products are generally good. We got better stuff here in asia, but I'm just talking about good products I've worked with before in the US.
Since you're doing no CO2, a substrate with no ferts is preferable. Probably a natural looking light-colored sand would be most appealing. Make sure it's something inert, made for freshwater not salt.
For lighting, buy yourself an attractive looking desk light, something that looks like this:
and use a Spiral Compact light.
10-19watts is what you want (19 is kinda strong though), ideally with 6500 kelvin lighting ("sun light" is a good label to see), or atleast 5000, less than 10,000. You can get one at a COSTCO for like $10 or something.
Finally, tie some common java moss to rocks like this:
arrange in the tank and voila! Done. Frequent water changes (like replace a small cup full of water every 2-3 days) will keep a certain amount of CO2 and nutrients in the tank for the moss. Light should be on for 6 hours a day.
Eventually (after a month say), introduce some shrimp (Cherry Shrimp are the best for something like this), and possible 2-3 VERY small fish like Neon Tetras, or 1 betta.
Do the above, and you'll have yourself a very nice beginner planted tank.