I think we could pick a sport with a lot of events and funnel money I to it, encourage kids to do it and we could have success. I listed a few countries above and what they did with 1 sport they chose.
If you really want to win a lot of medals, pick individual sports that give out ridiculous numbers of medals, like swimming and gymnastics. Swimming gives out 96 medals, for various distances, stroke styles, relays, medleys and medley relays. And the same handful of athletes can contest them all. Could Phelps win 20-odd gold medals in any other sport? Not a chance.
Likewise, just pick a minivan full of teenagers, train them to be gymnasts, and reap a rich harvest of medal chances in all the categories and subcategories of that puzzlingly popular sport. (And become adept at politics to keep the judges on side.)
By contrast, look at the resources required in hockey. Run tryout and training camps, choose a team of 25 world-class millionaire athletes who are accustomed to the best of everything in training and travel, assemble an elite coaching, training and medical staff, and acquire and transport a boxcar full of very costly equipment. Play numerous games, perhaps in different cities, over two weeks. If all goes well, you'll win one medal.