What do you look for in a forklift?

Most tilt bed tow trucks will move them for you.
Remember a 4000# lift has a 4000# counter weight.The hole thing will weigh around 6000# or more.
Had a propane 1953 Tow Motor brand in the 80"s. Hard rubber tires. Did not do well in gravel/grass/dirt.
A air tire lift will handle those. Some may be jell filled instead of air and work real good.
Side shift is nice but not necessary. I worked on lifts in the 80's both propane and electric used inside for warehouse work. Batteries last as much as 10 years or more if maintained. We had Hyster,Clark,Tow Motor,Raymond to name a few.
I'm sure newer models will be much better than my old '53 but it did get the job done.