Stages refer to the number of steps that the water goes through during the filtration process. This depends on the particular unit and is usually determined by the condition of the water going in.
Being from Oak Lawn, I'd say you shouldn't need more than a 4 Stage RO/DI for your water. That's 2x Prefilters, 1x Membrane (3 stages) and a DI stage (stage 4). You can get a 5 stage (3 prefilters, 1 Membrane, 1 DI stage) if you wish that will reduce the amount of prefilter changing you need to do.
Now, me personally, I used a 5 stage RO unit (When I was living in Burbank) and didn't bother with a DI stage as the water coming out of the unit was clean enough for my tanks w/o the DI.
HTH,
RandalB