Free: Contests & Raffles.
8K is a tight budget. I second the tractor approach as you won't have issues with traction, and you can operate 2 implements at once. I would think something in the 40HP would give you close to 2K lifting power. I have an LS MT235HE. It is 35 HP and is Just shy of 1,700 at the pins. Turns on a dime and works in tight places though.A neighbor has a skid-steer with a blower on it that bailed me out a couple times before I got the tractor. it had "summer tracks" on it and would get stuck on snow in a low spot. never took more than a small nudge to get it going again, but those tracks would just spin if it stopped in the wrong spot.But 8K is a budget # you are going to keep hitting up against... 2-3 times that will get you a nice machine.I just unloaded a truck full of lumber onto the forks on a pallet last weekend. I just dropped it in an out of the way place, and then when I am ready for it I will pick it up and move it to the job site. Pretty handy!
If one of the primary purposes is moving logs onto your sawmill, it might be better to look at a grapple vs forks.Take a look at some of the posts on this thread, it might give you ideas. There is a wealth of knowledge on Tractorbynet.https://www.tractorbynet.com/forums/threads/tractors-and-wood-show-your-pics.303328/
You may want to check out https://murphyauction.com/ they are having equipment auctions this weekend.