Another low tech newb question

Its going to take a LOOONNGGG time to get any major density, but...those cheapo fixtures can pull it off since your going to want to get low light plants. Crypts, Anubias, Java Fer, etc.

As far as the word "thick", that may be a long term outcome, but if I were you I would just shoot for a good planting and good presentation and layout. Some small dosing of fertilizers will also help with growth.

Dosing excel as a CO2 supplement will also help, but it will get a bit $$$ over time.

Yup things will grow but it will be very slow. gmccreedy is correct when he/she says concentrate on good planting and good presentation and layout. Because you are doing a river theme most of your tank will be driftwood so having plants grow slowley isint a huge deal.
Research plants that can be easily propogated such as hygro. I have had it in my tank and they grow very fast for a low light tank and to propogate you simply snap the top off and plant that. In about a year you will go from one plant to maybe 6 depending on how tall you want them. Having lush growth doesnt need to be an expensive endever.