My $0.02:
A Stumpjumper hardtail is nothing like the Stumpjumper FSR as far as design intent is concerned. The Stumpjumper hardtail is an XC race weapon, whereas the Stumpjumper FSR is much more 'trail' bike, bordering on 'all mountain' (especially the EVO models).
If you truly want to get into DH and 'jumping', and want to use a hardtail to do it, something like the Niner ROS, or Diamondback Mason (or similar bikes) would be where I would suggest you look. These are heavy duty (and just plain heavy) hardtails that like 140mm travel forks and have short-ish chainstays to make them very 'playful'.
If you're going to go FS, I would go with 120mm to 140mm travel in 29" wheels, or up around 140mm to 160mm in a 26" wheel bike.
Full suspension: As for budget, and I'm generalizing here, if you can get into the $2500 to $3000 range and shop carefully, you can get into something pretty decent. From $2000 to $2500, you have to shop VERY carefully, and from $1500 to $2000, you can count on probably upgrading the fork and/or wheels at some point if you regularly push the performance envelope. Brakes can be a crapshoot in any bike below $3000 (and several that cost more than that at times), but especially in the $1500 to $2000 range. The drivetrains on $1500 to $2000 bikes can be pretty serviceable (as mentioned, it's the fork and wheels [and brakes] where bike companies usually keep costs down).
Hardtails (above entry level): There are some OK hardtails that go for $1200 to $1500, some pretty good ones between $1500 to $2000, and very nice hardtails between $2000 and $3000.
Keep in mind that used bikes do not have a warranty, and some boutique brands only may have a 2 year warranty. Some big brand FS bikes have different warranties on the main triangle than for the swingarm. Point being, if you buy new, be diligent in knowing what the warranty will be as that is what will cost you more for new vs used and you did mention riding DH and 'jumping' which are two activities that are more likely to have you needing that warranty if you ride that way regularly. It's probably not likely, but it is certainly possibly.
If your tolerance for risk is a little higher, then you can certainly score some nice used bikes at a significant cost IF you shop wisely and carefully. And above all, make sure the bike you get fits you well. A bike that doesn't fit right isn't a bargain at any cost.