You could go with a DIY set-up, but IMO in the long run this costs more than a kit. Anyway, an example:
Mr. Aqua 3 gal bowfront
-$26.99 (next size up on marinedepot.com is 7.5 for $41.99.
Fluval 13 watt light
-$36 (but free shipping)...this light is probably too strong for a 3 gal but if you want something smaller you'll probably have to go DIY and that can be a pain.
-$8.52. I honestly don't know anything about this filter but it is rated for 3 gal and inexpensive, so...
-$18.25 (might only need the 4 lb bag for a 3 gal)
So you're at about $90 for this set up assuming you get the 3 gal tank and the 8.8 lb stratum. This doesn't include any ferts (Floursh, possibly Flourish Excel, root tabs), plants (hopefully you can get some cheap ones...I've spent a fair amount of money on plants so far!), a heater, and a cover for the tank.
If you want to do plants "for real" as in, not just a java fern and a moss ball, it is unfortunately going to be expensive. Especially if you want a bowfront, all glass tank, because those aren't usually available in starter kits.