Most cheap big-box store pumps won't even deliver the pressure that you need for road bike tires.

If you're using the gas station's compressor, BE SURE to put an accurate tire gauge on your tire. DAMHIK... When you get your own pump, you can check the accuracy of your pump's gauge against your standalone gauge; if there's a large difference, check it against two or three other people's gauges and use your instinct and judgment as to what's really accurate.

I take it you need a pump that will easily accommodate both Schraeder valves (the big rubber spring-loaded ones that come on fat tubes like your beach cruiser, same valve type as on cars, motorcycles, and lawn and garden equipment) and Presta valves (the skinny metal screw-type ones that come exclusively on skinny bicycle tubes)?

$35-40 at your LBS should get you a good-enough pump, but ask them what they recommend. Spending much more than that will get you rebuildability, the capacity for super high pressure tubular tires, a certain amount of bling factor . Most inexpensive floor pumps claim they'll work with both types of valves, but some are easier than others. I've had good luck with my Specialized Air Tool Sport.