Welcome to the hobby! This is the right place to come to... I recommend diving into the forums and just reading about what your interested in...you'll learn a lot.
With respect to RO water, its not an absolute must like in saltwater.
Your lights will likely be okay if you were using them for corals. But be careful you probably have more than you need. If this was a car I consider the light to be the gas pedal. You can go faster in terms of growth but if things go wrong the faster it will happen, and by wrong i mean algae.
Do some research into plants. And the plants that you picked up at the river. The type of plants will dictate what substrate you need and how much light, ferts, and if you need c02. For example, I recently went to a low light, low maintenance tank growing ferns, anubias and crypts b.c. i got sick of trimming. I switched out my substrate for pool filter sand which is inert. I does ferts still and will be putting grow tabs in for the crypts.
If you are starting with the 10 gallon I'd go for the best you can afford. You wont need much for a 10 gallon and again, it will depend on what you are trying to grow. You can go from inert pool filter sand, to dirt (yes dirt) - look up Dianne Walstead method- or the high end Aquasoil by ADA. There are also plenty of others in between.
Cycling with plants is usually shorter..again depending on the type of plants and how many. They plants will use up at ammonia and nitrates. In fact, we dose nitrate for plants as part of fert regimes (look up EI or Estimative Index developed by Tom Barr).
People tend to advise to plant heavily when starting out. I agree with them. It shortens the cycle and makes the tank look nicer faster.