We live in Virginia, and our basement used to get a significant amount of water in heavy rains. If I were you, before I spent a dime on flooring or anything else down there, I would find out definitively where the water is coming from, and how it is getting in, and then fix it. The prospect is scary, and can be expensive, but the potential for mold and mildew that you can't see, and for structural damage to your foundation from water piling up against the wall, or standing in the wall, even when it doesn't flood, is scarier. We took off some cheesy masonite paneling and discovered that the insulation and the wallboard underneath was black with mold up to our shoulders. We learned from two engineering reports that our saturated soil was actually putting so much pressure on the block foundation wall that it was beginning to bow inward. Our contractor dug down to the footings on two sides, jacked the wall back into position, added steel supports to the inside of the foundation wall, put in a new drainage system, including underground extensions of our gutters into the drainage pipes, waterproofed the walls on the outside, added a layer of this plastic stuff that carries water directly into the footing drain, and backfilled with soil that drains well. It was drastic, and expensive, and it worked like a charm, and now we are the only people in our neighborhood who have a dry, dry basement. It was worth it. I bet you can solve your problem more easily than that, but I urge you to at least find out. With all best wishes...

If your lot is perfectly flat - you may need a sump pump installed in the basement. That sump pump would only run if there is a lot of water around the house and the exterior french drains get overloaded. We had a sump pump in our last house in the basement. Occassionaly when it would rain a lot - it would run. I think it helped to keep the basement from flooding. I would not want to have a new home and have to have interior french drains. Many times until the landscape/grading etc is complete there is the potential for water/dampness in the basement. Once the water is gone - for now I would run a dehumidifier to help dry out the block and concrete - otherwise you may get mold/mildew

Clogs typically happen at a trap. Your 4" main soil stack would probably never get clogged, but if you are worried you could in theory put a backflow preventer between the basement bath and the main soil stack (allow access for maintenance). They make 3" and 4" backflow preventers. It honestly shouldnt be needed though. I would recommend installing a backflow preventer where it would protect all your drain lines from a city sanitary backup and a watchdog alarm near the floor drain in the basement so if the city backs up and the water you use backs up in the basement the alarm will go off so you know to stop using water.

If it persists you might have to install a foundation drain system. They are usually absent on old houses. They can trench around the outside of the house and install a perforated pipe in gravel to carry water away from the foundation. Another way is to cut the basement floor around the outside wall and install a drain pipe loop leading to a sump that will pump water out.