Please, please listen to what the folks here are saying about bow weight! Traditional shooting requires practice (lots of it!). If you start with a 60 pound bow, you will risk injury (joints and tendons), poor form, and worst of all, a switch back to wheels. Just because you can draw and fire a 60 pound bow a few times, don't think it is the right weight for you.
If you are drawing 26 inches then a 50 pound bow would put you at about 44 pounds, more than adequate for whitetails. Are you sure you draw 26 with a trad bow? Remember you will lose about 1 1/2 inches in draw going from wheels to trad. If so, a 50 would be perfect. I like longer bows because there is less finger pinch and they tend to be more forgiving (I need lots of forgiving).
I have a 55 pound longbow, and I love it, but I can't take a steady diet of shooting it without ending up with tennis elbow (tendonitis). I draw 28 inches (traditional) so I am pulling all of the 55, but you would be at 54 at your draw with a 60 pound bow...too much for daily practice. With my Kota 48# or Bear 45#, I can practice as much as I need to without much pain (still some if I get carried away).
Shot placement is much more important than bow weight. Unless you are hunting moose or grizzly, which I wouldn't recommend for a trad-novice, you will be much better off with a bow under 50 pounds.
One final thing, as you practice and develop good form, you may find that your draw length grows too. Mine went from 27 to 28 once I got my back muscles working properly. That will add about 3 pounds to your bow, so at 27 your 50 pound bow would be 47. Even at 44 pounds, your arrows will blow right through the chest cavity a whitetail at 15 yards. That is traditional bow range.
Welcome to the fold. You WILL become a better hunter using recurves and longbows. That's what it's all about!