I might think about putting in commercial carpet squares which are inexpensive and can be replaced one by one if you have another leak/flood.

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Shop vacs and dehumidifiers to get rid of water to start with, then removal of any soaked insulation and drywall lest you have a mold farm in your basement. Once the emergency stuff is past then figure out where the water is entering. If you're lucky it will be poor drainage and grading, which is relatively easy to correct. Fix any deficiencies and then wait a season to see if you've solved the problem. If no then consider something like a french drain leading to a sump to keep the water out of the living space. Don't invest anything in finishes or decoration until the water problem is resolved, that's just money down the drain, as it were.

Once the space is reliably dry I'd stick with an impervious floor like ceramic tile or epoxy paint with area rugs that can easily be pulled out if water problems recur.

The floor needs to dry completely befor anything is put down IMO carpet never in a basement that might flood. Right now you need to fix the issues before any other things are done As said above this needs to be fixed first .An indergorund spring is ahuge issue and I have no expeience with thta particular issue but get a pro to make sure all the water goes somehwere not in the basement . A sump is great but not if the water is under the house and coming up. Often this issue needs some serious work on the outside to make the basement dry and can be expensive no way around it. We put dricore down and then a viynl plank that attaches to each other and can be rolled up and reused in case of a flood .It is called Allure from HD not sure if they still do it ours is 18 yrs old we have had 2 very minor floods in one corner the floor survived well and we had to replace a few pieces of dricore but of course not a huge flood . We have since figured out the issue and had it fixed so last 5 yrs no water .

Close friends have the same underground spring issue - when they redid their basement they were told that drain tile and sump pump would handle the water and that wasn’t the case, it took a very large project digging trenches around the perimeter of house, installing drains for their basement to be dry - agree with the above advice to wait until you are 100% sure the water is being taken care of before spending anymoney on the interior

We had a flood in our basement and it‘s really important (re: mold) that everything is completely dry including any dry wall, base boards and foundation affected. If anxious to redo, rent a large commercial fan.