The sidewalls on the tires will list max pressure. Ideal pressure will vary based on the tire, your weight and what surfaces you ride on.

I can not feel a 10 or even 20 PSI difference in my tire pressure by squeezing the sidewalls but can definately feel it on the road. You need a floor pump with gauge for home use. The mini pump is just to get you back on the road if you flat during a ride.