water sensor are prone to false positives, from things like wind.
One issue with your desire, is that most door/window sensor are deisnged to reside indoors, not outdoors. Doesnt mean there aren't solutions, but there will be more limits.
If this were my house, I would probably not put fence gate sensor in, unless I coudl find some cheap options. I would go with a motion sensor out by the pool. You coudl go with a camera if you wanted, but just a motion sensor would work. I would get a Hubitat (or Smart things) based system, and you can create lots of options for your whole home. You can set up rules to trigger puch notifications to yoru phone if the motion sensor rings, or even have a siren make noise in the house. But along with the hubitat system doing motion, you can get smart light switches, light bulbs, door locks, etc. You can set up rules to lock doors at ceratin time. Turn lights on and off at certain times. Use your phone to determine if your home is occupied or not to change settings. These systems can be controlled via your phone, and require no monthly fees.