The Winchester 1866 Yellowboy was in the original .44 caliber, the .44 Rimfire. That caliber is long gone, as is Winchester as a manufacturer of the 1866, but Uberti still makes them (and sells them under a variety of names in the USA)and chambers them in .44/40
The also make a very nice Winchester 1873 clone, in many variations. Here is the all-around 20" version, again in our caliber of choie the .44/40. Both about $1300 list.
And as for handguns, go with a matched pair of these beauties! US Firearms SAA - many options, including .44 special, but the .44/40 is too. $995 list is steep, but quality always costs. Made in the USA (in the old blue-domed Colt factory in Hartford, CT, amazingly enough!) Get one to match your long-gun!
Now your set for Cowboy Action Shooting, except for the scattergun.
The targets are so close and large that I see absolutely no point in punishing myself with anything heavier. I use a fairly heavy load in .38 sp and it's more than adequate. Even a bonus round where you could use the rifle to knock down the shotgun targets was no problem at all.
My skinny little 22 year old daughter used my firearms for the first time (her first Cowboy match, AND the first time she had fired any of my Cowboy firearms) and shot a clean match. She was slow, but she shot a clean match!