Should I level my basement floor if installing a subfloor?
How old is the house?

This sounds like an old house given a 1-2" deep puddle and painted concrete.  

You should consider that :
 - the slab is probably too thin
 - inadequate drain rock under the slab
 - no insulation under slab
 - lack of radon / vapor barrier under slab
 - the exterior perimeter drain may be clogged
 - sewer service pipes in slab may be close to lifespan
 - consider a backup sump pump on a hydrocheck HC6000v2 (non mechanical float) 

How long do you plan to keep the house and how large is your budget and timeline?  Doing this properly can be expensive.

Quick and Dirty would be to level it to within 1/2" over 4'.   Certainly fill any depressions.  Choose a waterproof vinyl plank flooring.  I like the 6mm duraclic from lowes.  You probably want to put down a 6mm poly vapor barrier under the flooring and tape seams to keep out radon.  Having gone down the high end path before quick and dirty appeals more and more to me.

If the house is newish and all the above items to consider are good and you have budget you could take the pro approach and flood the entire floor with self level.  This will yield the best result but is the most expensive option.  Have to worry about door heights, etc.