Mechanical watches need servicing every 5-10 years if you want them to keep reasonably good time, the cheapest ones that are sort of outdoorsy would be some of the seiko 5s, but the water resistance on them isn't great, you wouldn't really want to swim with them. Orient mako and ray are more out friendly but again they need servicing after a while, timex marlin maybe worth a look too if it has to be mechanical.
If you can accept a battery change every few years (really easy to do, see youtube) quartz watches are cheaper and usually better water resistance at this price. G-shocks are what you want for function, though if you would prefer something a bit more traditional, timex scout, weekender, expedition lines are all quite good water resistance, any quartz watch you like with decent water resistance will likely have the same movement powering it though, so just take your pick.
