a manual has less moving parts a proven long lasting design and, what most folks that really work an atv seem to find better and less down time!
are you looking at new or used atv's
as IMO< if you don;t know much about atv's, your at a BIG disadvantage looking at used one, very VERY few honest sellers out there these days and far too many lie about use, or ABUSE they used atv with!
when looking at NEW or left overs, I think staying under 6 k is going to be tricky, once you add in taxes and such!
I would stick to NEW foreman 500's manual shifts in a honda model
if you wanted to go other brand, my vote will be for a Yamaha grizzly in a 700 cc motor for your needs, costs will be about the same only the yamaha will have a little extra HP to afford you some pulling power and little heavier to control weight a little better>
both great long lasting models IMO!
power steering is also nice, everyone that gets it will never go back so they say, I have never owned one with it so?? just saying, food for thought, working slow in rocky terrain I can see it being helpful and maybe worth having!