Rigid bikes are fine on the road because with an adequately chosen tire pressure (I run about 88-90 psi* on my road bike, anything more would be excessive) and if the bike fits you well, you've got all the suspension you need. For any potholes / speed bumps you unweigh the saddle a bit and absorb the hit by letting your body move.
Of course it's going to depend also on body weight, you probably will at least need wider tires if you are overweight to find comfort, and again - you would want to try with lower pressures and then work your way up.
*Pumps can be quite inaccurate. After calibrating mine, I found that what I thought was 105 psi was actually more like 95.