Have you tried sealing the basement?Does it have finished walls or block? If it has block walls still ,you can try rolling block sealer on and see how that works.

We've done this, but I'm afraid I won't be much help with making it better. Our room in the basement in our previous home was a photograph darkroom and we just built a higher platform to stand on when the basement was wet. If you mean a permanent room like a bedroom, I'm sure there are sealers to keep the water and dampness out.

If you're going to turn your basement into a room one thing you should do is make sure the sump pumps are covered. Sump pumps aren't always sold with covers, so many people don't realize how important they really are. A cover will keep pets, or even mice, out. Covers will also keep any dirt, dust, or other debris out. That helps keep the pump running longer and better.

Since pumps are run usually on house current (sometimes generators) the safest thing is to cover them to prevent possible electrocution hazard.

You probably have already thought of this. A tile floor is a better idea than carpeting if you know you'll get water over.

You could also try a raised floor, but that would depend on how low your ceiling is. Otherwise, I would go with either tile or cement paint.