LRH, perhaps there is the plan of getting an older sound healthy horse, of good hardy peasant stock, who is of an age wherein they can do what you want, but if anything other than mild age-appropriate arthritis, manageable with Previcox or Pentosan, was going show up, it would have shown up already? 
That is my plan, but I don’t show, so it’s easier to find an appropriate sweet, enjoyable, uncomplicated partner for lessons, trails, and the occasional camping or beach trip, or local hunter pace. I lost one perfect horse at age 27 a few weeks ago, after 10 years of very fun ownership with barely an issue (total vet bill over 10 years, not including the last 8 hours, $1800). I’m going to look at someone tomorrow, and again next weekend – both mares in their late teens, never (supposedly) had a lame day in their lives, all-around horses with good basic training and sweet temperaments. That’s all they need to bring to the table; my trainer gets to do the rest. And, my saddle cost more than these horses. But, I have probably just jinxed myself! Oh noooooooo!
But, I know it is different when you want to show. Or if you are a good rider (lacking talent myself, I am oblivious to lack of it in a horse).
By any chance, are you in eastern Massachusetts? Your description of horse ownership is dead-on for this area.
Good luck!
