The first thing everybody notices about my phone is that it's covered with grip tape on the back and sides. Some people think this looks uncool, but I think it looks much cooler than a phone with a cracked screen from being dropped, which is what I'd have otherwise.
However, there are significant differences between grip tapes. I've used several different kinds, and I'll summarize them here for you.
The medium grade is grey. It is coarsely textured, but is all plastic and does not include any sand or grit particles, which is good. I find it a good texture to grip, but it's coarse and thick enough that it can cause a phone to hang up on fitting into a tight case. It does wear with rubbing, and will probably need replacement after 8-12 months of use. The light grade is clear and much thinner, and I have not found it to impede the insertion of phones into cases. It's probably the better bet if you're going to get one of the two.
The part number for a 1" x 60' roll is of the medium/gray is "7739"; the same size roll of the clear/light is "7751". You should expect to pay about $25 to $30 for a roll, and a single roll is probably a lifetime supply for you and your whole family. It is also available in other widths. Vendors come and go, so just search for "3m 7739" or "3m 7751".
I'm aware of only one vendor of the Right Thing, which is Egrips (manufacturer's label) and Gecko Strips (their consumer division). You can buy a 10' roll for $20 - astute readers will have noticed that this is 6-8x as much as the 3M grip tape. If that link has broken by the time you read this, search for "gecko strips univeral" and then look for the roll. All other precut shapes are many, many times more expensive.
Still, this tape is much cheaper and easier to find, and it might be good enough for what you need.