Recommend a good contractor to install basement flood control in Des Plaines Illinois residence not too expensive. What should I expect to pay (range?)

Get 3 quotes for the work you want done. We have no idea of what your problem may be as "flooding" covers a lot of bases. River flooding? Drain runoff?

Sewer backed up in hard rain 4 weeks ago.

'Good' and 'not too expensive' often don't go hand in hand. Especially in dealing with drainage. It's a complicated subject and you might want to read all about it before even calling contractors, so you can be an informed client. Curtain drains, footing drains, sump pumps, trench or French drains, various kinds of sealants, crack fillers, and so on. There are new coverings for poured concrete walls. There are new-ish ways to wrap the footing drains in gravel and landscape cloth and attach it to the wall. Many contractors aren't current. When you get quotes, if they aren't specific about the work, don't hire them.

Sewer backed up? Maybe you just need it videotaped and routed.

Would you be on city sewer or a septic tank? If on city sewer does your rain water run off connect to the sewer instead of running out on the ground? I may have a solution but until you give me more information I can't help. Regards, Tom