I think high intensity interval cardio training (http://en.wikipedia.org/...ty_interval_training) can be invaluable for a quick recovery when doing 2 in 2 out rotations. Steady state cardio is good for stamina for long days training. For strength training anything that works the shoulders (particularly pushups and pullups, safer than maybe using too high weights) and helps protect the rotator cuffs would be good. For general flexibility and strengthening the core something like yoga or pilates would be good. You can buy a foam roller cheap and do some basic pilates exercises at home that would be good for strengthening the lower back.
As your technique improves your shoulders will take less strain flying head up, however anything you do to protect the rotator cuffs now will benefit you down the line (particularly if you use risers when flying your canopy). Any good flying is initiated from the core not the extremities (it doesn't matter what the wings are doing if the fuselage isn't presented correctly).
For me cycling to work gives me a pretty good basic level of fitness, I just add some gym time to supplement it strength wise.
flying in the tunnel works out so many different muscle groups at once that its hard to pinpoint a particular group to work out... however, i would recommend trying non-conventional exercises... think of the relative wind and where it is hitting on your body in a certain body position... drawing this out (stick figures) in the position your body would be in helps a lot as a point of reference, then draw vertical lines (as if it were the wind) throughout to see where the wind would be hitting your body... after that, come up with an exercise that would counteract the "wind" ex: for working out your shoulders for sit-flying: hook up resistance bands/ bungee cords to the roof which in this case would simulate the wind (2 for each arm ) one band goes around your forearm and the other around your bicep with your arms bent at a 45-90deg angle(put padding or wrap the bands with a towel, so it doesnt kill your arms) then squat down as if you were sitflying, causing the bands to stretch and pull up... remain in the sit position and move your arms up and down at a slow speed, as if you were flopping your wings doing repetitions... by remaining in the sit position, it would also help you develop those upper back/shoulder muscles you never knew existed and will work out your thighs... I hope this helps... let us know what you decide or what ends up working for you... Blue ones *Itchy