I run Schwalbe One (25c) tyres on my carbon Powertap wheels (they aren't tubeless ready) and they've been great.
Previously I've used Bontrager R3 Tubeless tyres and they were fine, just had one puncture I noticed, a screw through the sidewall, and it nearly sealed the massive hole, but not quite.
Just got some Schwalbe Pro One Tubeless 25c for my Dura Ace wheels, hoping they will be as good as the non-tubeless ones. I managed to fit them without levers (first time for tubeless) and they sealed really easily. The Shimano valves don't have removable cores, making adding the sealant a pain, but I just pour it into the tyre carefully before I fit the last few inches, and then make sure it runs round to the bottom before fitting the last bit of the rim.
I use the Bontrager sealant (bought a big bottle online) and I read in tests that it didn't dry out in a year and was one of the best performing, so I've stuck with it. I've taken tyres off after a year and found plenty of sealant still liquid. I will worry about refreshing the sealant when/if it stops sealing, I think I would probably replace the tyre after two seasons anyway.
I bought a fancy Bontrager track pump, which I can pump up to 100+ psi and then dump the lot into the tyre in one go, which makes fitting tubeless tyres much easier. Before that I burned out an air compressor and nearly gave myself another stroke trying to seal the tyre with a normal track pump, while the sealant pissed out the sides!
My wife's new bike (Specialized Ruby) claims to have tubeless wheels and tyres (2Bliss?) but came with tubes and without tubeless valves, so I guess I need to buy some valves. I'm not sure I like the specialized tyres, they have a minimum pressure of 100psi on the sidewall, which seems daft for 26c tyres. Tempted to bin them and get some Schwalbe Pro Ones in 28mm, but hate to waste brand new tyres!
I would feel much safer with all the family running tubeless tyres, seems less chance of a blow out at speed and also less chance of the tyre coming off the rim. Can always fit a tube if a puncture doesn't seal, although it would be messy and quite hard work by the road side.
Geoff