Most if not all of them have a humidistat on them which you can set to whatever level you want. It will turn on when it needs to and off when it reaches the level you want.
Keystone White High Efficiency 50-Pint Dehumidifier with Electronic Controls https://www.amazon.com/dp/B00IJYH02U/ref=cm_sw_r_cp_api_i_BdlcEb7AX36R7
This is the one I have, seems to work fine. Costs about $1 per day if run constantly.
I have this one. It also has a built in sensor but I found that it read the humidity as much higher than it actually is (according to my other sensors, at least) and therefore it wanted to run all the time. I now have it plugged into a smart plug which uses an automation triggered by Abode's temperature/light/humidity sensor. I've found this has the dehumidifier run anywhere from 2-5 times a day which uses less electricity than before and still maintains the humidity level I'm looking for. (Sorry for the information overload!)
It depends on your basement! We're in New England, and purchased a dehumidifier for our unfinished basement on the advice of our home inspector, who recommended keeping the basement at 30-50% humidity. Once we set it up, most of the "musty basement" smell disappeared, so that was nice. Definitely go the extra mile and set it up to automatically drain.
We purchased this one and have been happy with it. Check to see if your state has any rebate programs (we got $30 back for purchasing an Energy Star certified one).