We have gone the shirt route with my extended family and it is hardly worth it for the griping and groaning we've gotten from a few of them. You should probably determine what about the matching shirts is so appealing to you and then let that give you some direction Maybe you really want them for the photo, or you'd like for everyone to have a nice souvenier, or you'd like for other people to be able to recognize your group members.
Once you've figured out what's most important to you, here are some suggestions:
1) If you don't mind shelling out some $$ Lands End can embroider your design on their shirts. Then everyone will at least have a nice shirt.
2) If you are ironing on a design, let everyone pick their pastel color. It won't be quite so "matchy" but still coordinates nicely.
3) Taking that idea a little further, you could let everyone iron their design on whatever article of clothing suits them - maybe a hat, a tank top, a denim shirt, whatever. Again, everyone gets a little choice and you don't look like the mickey mouse club
4) Apart from logos, in our family we have had the most success (and even that wasn't total success) by requesting a color scheme for photos. One year we had everyone in denim, black, white, and red. One year it was denim, khaki, white, and red.
5) If your heart is set on all matching tee's, then I say spend as little as you can for the shirts and make a cute design to iron on. You're right, most people will only wear them once.
6) Some people really don't like their names on their shirts and it's considered a safety issue with children. (theoretically, strangers can lure them away because they know their names)
7) My niece had shirts made for our family for an Alzheimer's walk, and she inivited everyone to submit and vote on team names. Then she worked the chosen name into the design. That gave everyone a bit of ownership and some of us still wear our shirts often.
8) Be sure you buy the right size and style that is comfortable and flattering. Most of the shirts I've shed ASAP were too tight or too heavy in the heat.
Keep us posted on what you decide!