Basement – What are the options for a basement floor drain

From a comfort and water protection perspective, I think you'll find it beneficial to install a sub floor. I'd recommend one which allows for ventilation beneath it such as these 2x2 panels you can buy at Home Depot/Lowes

Dricore

This will give you a nice, warm "softer" surface to put your carpet pad on, and help protect from any condensation issues with the cold floor beneath by allowing it a place to form, and then with the proper ventilation openings cut into the subfloor (standard floor vent in the carpet to allow airflow) it'll dry out on its own.

The simplist solution to dehumidifying in an area with no drain is to use a dehimidifier with a built in pump such as this one:

It has a long thin tube that can be routed to an area with a drain (such as a washing machine drainpipe) or to the outside (through a window frame or a very small hole drilled through the wall). If to the outside, you need to direct it away from the foundation.

There are a few versions available and they tend to cost a good bit more than a simple tank type, but the convenience may make it worthwhile.

If you already have a good dehumidifier and don't want the expense of replacing it, you may be able to use an add-on dehumidifier pump such as this one

It is hooked up to the demidifier and then uses a thin tube to move the water in the same manner as a pumping dehumidifier.