A FW planted tank using SW reef equipment is actually done quite often.
There are a few things to look out for.
Even high tech, high light FW planted system requires much less light that you would use on a low light SW reef system. For example, if you were using a 4 bulb T5 fixture on a reef tank, you would typically use about two bulbs on a high light planted tank. The color temp of lighting for a FW planted tank is also toward the lower color temps about 6500K to about 10000K. Actinic lighting is almost never used on FW planted tanks.
You can use a sump, but with all the water flow and all, it will tend to degas CO2. In a FW planted tank CO2 is you friend, since it keeps plants growing well. Many FW planted systems supplement CO2 by various means.
RO/DI water can be used, but you usually need to build it back up. Also, you usually don't need the DI part, so you can save some money there. You'll see items like GH builder that you use to bring the water to the hardness you want. You'll also need to do the same thing with KH. Many planted tank keepers just use tap water, and add something like Prime. Personally, I use RO water and build it back up, as I feel I have more control.
Nitrates and Phosphates and such. In a SW reef, you are usually working to keep these as low as possible, to control algae. In a FW planted tank, you need a certain amount of them for plant growth. The trick here is to have the plants growing at such a rate that they out compete algae for the nitrates and phosphates. People that get into planted tanks, often add fertilizers to maintain nitrate and phosphate levels. It's quite a switch from a reef. You usually want to buy the GH builder and ferts in bulk and mix you own stock solutions. There are a some very elaborate methods of dealing with ferts in a planted tank. The good news is that you don't need to get that fancy.
Get your plants from LFSs that know what they are doing. There is a lot of fraud going on here, with house plants being sold as aquarium plants. May people in the hobby will sell for cheep, trade, or give away cutting of plants they have.
Obviously you will not tend to get the best answers about planted tanks on a SW reef forum. I recommend joining one or two of the planted tank forums. Here is one I use (offsite) -
http://www.plantedtank.net/
You see a few names that come up again in the hobby.
Tom Barr, who is one of the experts on the subject. He's got his own website here (offsite) -
http://www.barrreport.com/ Note - some of his newsletter stuff is not free.
Takashi Amano is the person that just about invented the "nature aquarium", which is a commonly used method for keeping planted tanks. He owns ADA which is a company that makes products for such tanks. You can see the company site here (offsite) -
http://www.adana.co.jp/en/ Inspirational tanks, but ADA equipment is ultra extreme expensive, often even more that SW reef equipment. Amano has also written a lot of books on the subject. They usually contain fantastic pictures, because he is a photographer by trade, but the books are usually a little short on how to do it.
Books you might like -
Encyclopedia of Aquarium Plants by Peter Hiscock - Excellent information to get you going.
Ecology of the Planted Aquarium by Diana Walstad - Really gets into the science behind FW planted tanks. Book has only a few picts.
Good luck. BTW, depending on how deep you get into this, you may find planted tanks almost as much work as a SW reef. However, they do tend to be a lot less expensive to setup and run.