I was recently gifted a rifle from a relative and I'm trying to find some more information about ammo I can use, and care of the rifle.

Rifle Information:
Winchester Model 1873
Caliber 32-20
S/N starts with 39xxxxb - records date this to be an 1890 era production
My relative used it from around 14 up until last year for small game hunting. So roughly 40-50 years of use under this relative, and even more from past ancestors.

Ammo:
My relative informed me that I should only use pure lead, and slow burn black powder should I wish to use the rifle. I would like to maintain the functionality of the rifle and have it for not only an "above the fireplace" gun but also a good small-gun rifle as it's part of our family's history.

What are some safe modern alternatives to use as ammo while I compile reloading equipment for this rifle. Ideally, I would like to hand load rounds for this rifle, but currently lack space and money to invest into decent equipment.

Online I have found lead alloy cast rounds that I could use for reloading, but I am wondering the damage, if any, an alloy would cause over pure lead. I'm pretty sure I can find black powder without too much effort in my area, but I'm also wondering about a modern smokeless equivalent to hopefully lessen the cleaning that will be needed after each use.

Care:
If I recall correctly from others, black powder weapons should be clean often and regularly after use to prevent corrosion. Typically, I would use solvents and other chemicals on modern weapons to clean them, however, given the age of the rifle, I would want to try and avoid any damage chemicals may cause to it. Is there anything I should look out for when cleaning the rifle?