I think quartz is better in this case.  Casio Edifice, "Aqua Terra" 😃 is a stunning watch and very reliable. Not to mention that you can find it around £70-80 so you can buy a decent strap or 2 if you wish and still under your budget. 

I have a small wrist too, no problem wearing this watch. It's more about the lug to lug distance than the diameter. Go for it, you won't regret it!