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Casio MRW200. They're not too big, and they are very light. Not a G-Shock, but still a tough little watch. Good water resistance. Less than $20, so easy to replace, but still good quality.
I had the same search few years ago. Unless you need tide info, a cheap watch is great. Your priority should be the waterproof rating, ideally something waterproof to 100m. Even though you won't be getting anywhere near that deep, paddling and falling will have your watch impacting the water constantly, so you need seals that can handle that kind of sudden burst of pressure.
Other considerations are a face that's large and easy to read. For this reason I prefer analog watches, lcd screens can be tough in full sun.
I got a Casio off Amazon for like 15.
Loved this Casio - the little dial around the face was great because you could just turn it to align with whenever the section started and really easily see how many minutes had passed
I've worn this watch every day for 5 years. It's a little scratched, but not bad. Only $15 and has endured countless layouts. I can whole heartedly recommend this watch.
Casio Men's MRW200H-1BV Black Resin Dive Watch [link]
This is actually a great watch that fits your criteria. I use it as a swimming/beater watch. It looks way better than it's price and you can use the bezel as a timer.
Any generic quartz should be reliable to 1-2 minutes a month, just dont get it wet or expect the batter to last long,
I would invest slightly more and get a casio
This is also a decent option if you want to spend even less. It's nothing extraordinary, but it's just as waterproof and weighs less. It's the other watch I wear in the pool. I bought it when it was under $10 on amazon, because why the hell not at that price, so I'd recommend keeping an eye on it and snatching one up at least as a backup or just to mix things up a bit when the price goes back down around $10.
I bought a similar Casio. I'm rough on them. Mine has lasted a while. I figured for $10-$15 it would have stopped working or I would have broken it--and I wouldn't mind. Now I feel I'm playing with house money.
This is the one I got:
I believe it’s this one
Super cheap. This is what I have used in my nursing career.
> and not be a douche with a fancy watch.
-Posted from my iphone 8
Try this one out: https://www.amazon.com/Casio-MRW200H-1BV-Black-Resin-Watch/dp/B005JVP0LE/ref=sr_1_2?ie=UTF8&qid=1526576427&sr=8-2&keywords=CASIO+watch+sports. It has a rotating bezel