The Model 1873 in .22 caliber* is pretty rare (I have seen only one) and I would advise not doing anything yourself unless you have experience with antique arms work. Dollar wise, it is better to leave it alone than to make a mistake and do it irreparable harm.
You can use a good penetrant on active rust to prevent it from getting worse, and clean off the worst of the dirt, but that is all. Meantime use Google to locate experts in that gun. I do not recommend taking it to a gunsmith since most of today's gunsmiths have never worked on any Model 1873, let alone a .22. AFAIK, parts unique to the .22 are simply not available.
If you decide to have it restored, contact www.turnbullrestoration.com
and see what they say.
*This assumes the rifle is a factory .22, and not a gunsmith conversion.