I am 42 - vault 15' now (have 2 meets left this summer to go higher

). I find that when I kick in my training I can get tendonitis very quickly. Once I get it, it is difficult to get rid of. So, work up slowly and consistently - don't start running 15 200's the first day. Ice your Achilles and hamstrings whether you think you are getting tendonitis or not. If you are like most vaulters (at least my opinion of most vaulters), once you get started you will want to go full blast. If you do that you will explode. Be patient and work up to it. Stretch every day.
As I get into better condition, I do less distance running and more speed work - down to the point where I don't run more than about a mile as a warm up before speed work (200's, 100's, 50's - I have dropped 400's because my Achilles seem to get really sore from those). As I decrease my running distance I add biking to help keep my weight down - I can gain weight very easily now. I am 5' 7" 155 so I may be near your size if I remember other threads correctly - I was 140 as a senior in college. I find I can do quite a bit of biking and not get tendonitis, so I bike if I feel I need a couple of hours of conditioning.
Weights are always good - not 4 rep sets to start:) Maybe 15-20 reps to start - and not to the point of failure. Stiff legged dead lifts for upper hamstrings, leg curls, lunges, let extensions, standing calf raises, seated calf raises - upper body also, but make sure your legs are strong enough to vault or you will get injured and it will nag at you. Body weight exercises are good - do standing calf raises on the stairs - start with both feet at the same time - work up to 1 leg at a time.
So, I would start with a light jog and some light weights. Slowly run a bit harder and hit the weights a bit harder - listen to you body as to how fast to build up. After a couple of weeks add some light 200's. I would not do huge amounts of distance - for me it just beats up my legs - as you get in better shape add more speed work instead of increasing distance. I am not sure when to start vaulting - but when you are ready start with short run - like 2 or 3 rights (I am a lefty). No 10 step runs for a while.
My opinion is that at 39/40 you can vault very high. I think you will find that your body will respond pretty quickly as long as you get consistent workouts in. You can't pound yourself into shape like we could when we were in our 20's. The danger is that you will start to feel pretty good and add a couple of steps to your turn too soon.
I don't know if this is the right answer, but it works for me.
Hope to see you in Reno...perhaps my family will be up for a ski weekend.
Duncan