For a heavy guy to ride the stairs, there is only one cheap fork option: A good old Monster T.
Find it in good condition on Pinkbike for 300$, sometimes less off season. Easy to service, as simple and robust as a fork can be.
For the rear it is more complicated. The frame is built with a suspension travel ratio, in relation to the shock travel. That is the major factor and does require quite some work to mod. Let's say your suspension moves 3 inches when the shock compresses 1 inch, you have a 3:1 travel factor and it is way too much. 2:1 is too much already for good tuning when the rider is heavy, let alone the 20 lbs hub. You need a frame that has a low factor of rr suspension travel, or mod the suspension linkage on yours to achieve 1.5:1. Then you can start considering shock options, and most will do fairly good.