Welcome to the fire, Dakotamarlin.
A .38-55 normally uses a 255 grain bullet, and is an excellent short-range deer rifle. I wouldn't try it on deer at ranges more than 100 yards, but it will put them right down at short range.
Your rifle was designed for black powder loads, and you should keep your loads to black powder pressures and velocity. The steel is also relatively soft, and jacketed bullets may not be a good idea.
Before you shoot this rifle, you might want to have a gunsmith look at it and get an opinion as to whether it is safe to shoot. It is over 100 years old, after all.
Low pressure .38-55 cartridges are readily available. In fact, so many .38-55s are older rifles like yours, that I doubt anyone manufactures a high pressure or high velocity round for it. I would try a factory smokeless "Cowboy" load, like Ten-X as suggested above, to see how that shoots.
I think Ten-X has a minimum order for direct sales, but you can buy one box from Cabela.com to try them.
The idea of slugging the barrel is to see what diameter bullet you need if you reload for it, which is what you will have to do to obtain any great accuracy if the bore is oversize. Factory ammo won't seal well if the rifle is overbore, and you will get lead fouling and poor accuracy. A .38-55 is supposedly a .375 caliber, but, as noted above, that can vary from rifle to rifle.
Beartooth Bullets make bullets in several calibers. I suggest you look on
www.beartooth.com for information on slugging bores and loading cartridges. Also, Hornady sells a book on loading cast bullet cartridges, that is supposed to be pretty good.
I really wouldn't try to load for a rifle without reading a book first. It's not rocket science, but it is dangerous if you don't know what you're doing.
I enjoy the heck out of my antiques, and I'll bet you will too, with yours. Good shooting!