Yeah you should always practice, practice, and practice at home before setting out on the road, you can watch You Tube videos if you're not real comfortable with the concept.
What kind of tires did you have on the bike? The Gatorskins you're getting will be quite good, another thing you can do is add a set of RhinoDillos tire liners, these go between the tube and the tire, this will add another wall of defense before the tube. Don't bother with thorn resistant tubes though, these are quite heavy and accomplish very little. The RhinoDillos are a better product then the Mr Tuffy, but follow the directions because the soft end is suppose to be against the tube not the hard end.
The good news is that first you are willing to repair on the side of the road, that's great, better than some people! The other good news is that the more you ride and have flats the better you'll become at fixing them. Whatever you do don't get so lazy or so frustrated you just reach for your cell phone. I've been married for over 35 years, I can tell you that most wives do not want their husbands to treat them like they're your mommys, you have to learn to be self reliant and get things done by yourself, of course if you have a flat and it took you say 1/2 an hour to fix (though with practice this shouldn't take more then 10 minutes) you can call your wife and tell her you will be coming home a bit later than expected so she doesn't worry about you. So for the sake of your marriage learn to fix flats on the road. I can fix almost anything that goes wrong on my bike on the road, so I rarely call my wife, in all those 35 years of riding I've only had to call her twice, once because I got so sick with diarrhea (I even carry Imodium ad, but it didn't work) and I got too weak to pedal the remaining 12 miles home though I did try! The second time I called her was when I had a bike accident and was at the hospital, thought she might want to know why I was late. Anyway learn to be self reliant, this is true for other aspects of your life as well not just cycling.
As far as tire pressure goes there are a couple of websites that have calculators that you can use to determine your idea psi, for road bikes see:
http://www.dorkypantsr.us/bike-tire-pressure-calculator.html on this one scroll down to the second calculator and make sure you enter your bikes weight ready for riding including full water bottles, and your body weight clothed ready for riding, then simply enter your tire size and wham you'll get the correct psi plus or minus 5 psi. If you're riding a mtb or a bike with fat tires then see this calculator:
http://mtb.ubiqyou.com/