I really prefer the Fitbit One, although it won't give you everything you requested.
I love my Fitbit and it's been a big part of my weight loss. Whatever you choose, good luck and hope it's helpful.
I originally had the Ultra, and I liked it but the outer casing broke. When I got my refund, I chose the One, which I think is a newer version, and after using it a few months it seems better protected. It has a little rubber casing to protect it. Fitbit must have got tired of replacing broken Ultras
- a wristband
No, the One is a clip on like the Ultra. The Flex is a wristband, but I agree with movielover, I would find a wristband irritating. The One (or Ultra) is so tiny an unnoticable clipped to your waistband (or in your pocket).
- waterproof
None of them are waterproof, but they are water resistant (survives rain or sweat). I will say I dropped my ultra in the toilet (yuck!

) and it apparently survived the experience, but I wouldn't chance it. I've heard forgetting to unclip your one or ultra before sticking your pants in the washer is a common tragedy, but if you use it for sleep tracking this shouldn't happen, because you'll always unclip it for that.
- will tell me how far I've walked/run based on my stride
Yes. The one has a default stride setting based on your height, but you can easily adjust it online if you have a particularly long or short stride. There are different settings for walking and running.
- pace
Maybe. It's recording every step at exactly what time. So you can see charts of how "active" you were with a step count during a particular hour for instance. But I'm not sure if the particular # you're looking for can be found for a custom period. May be a feature I've never used.
- calories burned
Yes
- will link to my iphone and LoseIt
Yes to iphone. LoseIt supposedly too, but I've never tried it.