Yes, some vinyls are far easier to work with than others. In General, the heavier the vinyl the harder it is to work with. Vinyl doesn't have to be thick or stiff to be strong. Most of the vinyls now days weigh around 29 ounces per running yard. That means a piece of vinyl 36" by 54" weighs 29 ounces. Look at the specs for the vinyl. It should have an abrasion test rating. The more double rubs it can withstand, the better it is. I almost always use marine vinyls if I can. They have mildew resistant faces and backings, are oil and gas resistant, and have UV stabilized pigments so their colors don't fade.
The stretching is somewhat important. Most vinyls have a 2 way stretch, which means they stretch easily either from side to side or from top to bottom. It is important to orient all the pieces the same way when laying out for cutting. There are some 4 way stretch vinyls, but they are mostly used for specialty applications like ATV, motorcycle, and jet ski seats. The 4 way stretch vinyls have improved immensely in the past few years, but aren't needed for most jobs.
No one lives forever, the trick is creating something that will.