Basement – What humidity should I set the dehumidifier to

Humidity levels between 40-50% are what most people prefer in a house. So, I'd say that setting is fine. If you live in a humid region, you may want to keep the dehumidifier running down there all the time (and set it up to drain via a hose rather than having to constantly empty the bucket)

Welcome to the wonderful world (or mold) of wet basements.

Assuming you've stopped it for 3 hours after running 30 minutes:

So long as water is coming in, the dehumidifier needs to keep running on the humidistat. In half an hour you're pulling the easily available water in the air down to 50% - but there's an entire earth of more water wanting to replace that. Not going so far, there's plenty of less easily available to the dehumidifier water trapped in various surfaces and furnishings - sheetrock, concrete walls, floors, books, upholstered furniture...

That water will make its way back into the air as soon as the air is dryer than the item, but it may take some time to do so. In your case, evidently about 3 hours. assuming the deumidifer has a humidistat and can be set to hold a particular humidity level, set it at 50% and either dump the tank regularly or set it up so the water can go straight to a drain.

Assuming it's running for 3.5 hours continuously - if it feels dry, the hygrometer is, perhaps, bad. If it feels dank, the dehumidifer is having some sort of problem with running properly - sometimes they ice up excessively and stop effectively removing water - they should sense that and allow the ice to melt, but one that is not operating correctly might not do that. You may be able to see ice blocking the cooling fins if you look for it.

You would also expect to see water accumulating in the bucket if it's working, and not accumulating in the bucket (or doing so V-E-R-Y slowly) if it's not.