Short answer, only download and play FE:LH.
When you install the games into steam, FE:LH will be the only game listed, and the only game playable. If you want to play FE upgrade (Legacy) you must not install Legendary Heroes. And I am not sure this is even possible if you also have LH. I own licenses to play all three games - but LH is the only one that shows on my steam game page.
As to playing the legacy upgrade, it was/is a good game. But LH is much better. There is one area that I and a number of others have raised in the past as an issue. FE - legacy had the dynasty system where your sovereign could marry one of your heroes, and after a time, children would be born. Children, playable heroes with a mix of attributes, skills, etc. from both parents. Many of us liked this - but it did not make it into LH as it was buggy. So, yes, go with the last sentence of your post: "I believe I should just download legendary heroes and just play that, right?" 
