If you have come to this subreddit late like me then I can recommend the keystone 70 pint dehumidifier for your somewhat flooded basement. Its a frickin champ.
https://www.amazon.com/gp/product/B00CEZA018/ref=oh_aui_detailpage_o03_s00?ie=UTF8&psc=1
You'll also need a canoe and a viking hat. Will leave that to you.
I have similar problems in St. Louis, although mine seemed to be winter humidity more so than right now. I have a dehumidifier running in the basement at 55% and it's been doing a good job of keeping up without making my electric bill skyrocket. No signs of moisture down there. I also pushed dirt up against the foundation and sealed my gutters and roof where I suspected I has leaks and this has helped lower the humidity in my house and basement.
My house doesn't have exhaust fans, so I'll be installing one in the kitchen and the bathroom. I have all of the equipment bought, I've just been dreading doing the electrical. I haven't tried to get into the walls and ceiling yet since I bought the house last year. The old 1930's plaster makes it all a bit harder than current construction methods.
All in all though, if you are below 60% you shouldn't have mold growth but you might feel a little uncomfortable. A dehumidifier may help aid the A/C in removing extra moisture when it isn't running.
I bought this one in 2017, and it's still running strong. It even comes with an adapter that you can hook up to a standard garden hose so you can run it into a drain instead of having to empty the bin.
The only negative I can think of is that the bin fills all the way to the top. It's almost impossible to pull it out without spilling some water. My solution was to stuff a piece of Styrofoam into the float so it shut off a little before all the way full.
Edit: the black linked isn't the same one that I have, but maybe it's changed.
Mine looks like this one. It's $10 more than your budget. https://www.amazon.com/dp/B06XRKL3NJ/ref=cm_sw_r_cp_awdb_imm_t1_iIn.FbD16QMJT