Tires and Wheels for 5 lug 2WD - Need Advice

I've worn out the search function and have been reading posts on tires and wheels for 5 lug pickups. I'm wanting a wheel that will allow for a wider tire and make the truck a little taller. A tire dealer has told me that a 235/75 15 is the biggest tire that can be put on the stock 15x6 rim. He said that tire would "really fill up the space" left vacant by the stock setup. I'm afraid this tire might be too skinny so this is why I am now considering new wheels.

I'm thinking that 16x7 or 16x6.5 might get me where I want to be. I don't have any desire to lift the truck. I like the way it rides and wonder whether larger tires would improve the ride. I don't tow anything or go offroad. I drive to and from work and haul 2 or 3 loads of mulch a year. Any suggestions or advice would be much appreciated. I just want to do this right the first time. Thanks in advance!