I wouldn't have thought baseball boots were cleats - (do bear in mind that I'm an old man and may not be up with youth talk these days) but baseball boots have soft rubber soles, cleats are more like football boots referring to the 'cleat' similar to studsNo one has mentioned Baseball boots ( or cleats as the Yanks call them )- they are a great compromise between grip and comfort..
I have played in many forms of footwear: the main elements being comfort, support & grip
Most appropriate for general woods are army boots, or something similar such as walking boots
These provide ankle support, especially for rough ground, have good tread for grip and are comfortable if broken in for you. But some may find them heavy
If you want speed then the grip of any cleated sports footwear will give the grip for sprinting starts and to keep gripping while running. If they do not have ankle support then the extra grip can be bad (see note below)
If the cleats are hard this can give you zero grip on hard surfaces such as Tarmac or wooden floors, steps and bridges
I have a pair of old school jungle boots which are ideal in the right situation - but absolutely wrong in woodland. They are the type with extremely soft rubber soles (not tough ones for punji stick traps). The grip on wood of concrete is excellent, but I can feel every stone underneath
Water resistance is a matter of preference - the vast majority want dry feet so are after water resistance but with breathabilty to keep feet good. For paintballers we wear the boots for one days play, or a weekend with breaks. Military users in a warzone may be wearing them 24/7
Good socks and a regime of changing them is the winner
Some people are inclined to jump through rivers, or even walk down a river.
Unless you are wearing waders or seal the top then this means you will get them wet. Bring spare socks to freshen up, and if you are inclined to walk through a river then look at socks that will look after your feet
Note: the extra grip of cleats can be bad in certain situations. Depending on the intended sport/type of runner they are designed for some cleat designs are optimised for turning, EG to grip solid for the moment that when running in one direction and want to turn 90 degrees. If they do not have ankle support then your ankle could take all the energy in the twist of that turn - and you collapse in a heap