With that in mind I would suggest something mid travel around 140mm. And in true STW fashion I will suggest what I ride. I have a 2011 Specialized Stumpjumper FSR Carbon, the frame cost me £650 last year but as it’s 26″ they are cheaper now and obviously the aluminium frame are cheaper again. There are older versions of the frame with less travel and different geometry but I really recommend stretching your budget for one of this vintage.
The bike itself is fantastic, easily one of the best I have ridden. It climbs well and all works really well on rocky trails like Antur Stiniog black. Im sure there are better bikes but I’m not sure there are better value bikes.