What's the most I can tow behind 2014 Suburban?

The 2014 suburban only comes with the 6.2 in the Denali. The 2wd lists 8300 lbs. The awd and xl's are even less.

You will not pull the condo with that truck. Maybe a small trailer like this. Or something in the 7500 GVW range.

Best you may do is a 27 ft like this coachman apex..

http://www.coachmenrv.com/product-details.aspx?LineID=62&ModelID=291#Main

But weight the truck...

The limiting factor will be the non-replaceable factory hitch. I think it's maximum tongue weight is 1,000 pounds. Assuming a TT with around 13% tongue weight that puts your total towed weight at 7,692 pounds.
It's really dumb engineering that GM used such a hitch design. The power train in the Sub. is clearly capable of towing more.

Take a look at Lance, especially the 1685 - it had a TON of storage, but not a big shower. Or the 1995, or any other floorplan they offer.

Post the year of the vehicle.. ( Edit: I see the year in the header)

Then go get the truck weighed at a cat scale and post back the individual axle weights.

Then post the axle weights from the door tag front and rear.

Then post the tires max psi and weight rating at that pressure..

After all that we can then make a suggestion on what you can tow... This will give us your payload and what TW is within reason.

All other posts giving you a hard # would only be guessing, and I would not count on those opinions...