If the m1860 is a genuine antique Colt m1860 then restoration should not be on the agenda. Besides missing the wedge and wedge screw, the gun looks complete and in not too bad condition overall. Sure, it may not be a 2000$ piece, but if you "restore" it it will be worth less than it is now, while if you go easy, replace the wedge and screw and clean it up a bit value will go up some. In other words, if you restore the gun yourself and you´re not a truly competent professional restorer then you will ruin its value. If you leave it to a professional restorer, you will pay aproximately what a good condition original Colt m1860 would cost for the resto-work(2-3000$), and end up with a piece that is worth MAYBE 1-2000$ on the collectors market.
So, please don´t "restore" it yourself, just clean it up and replace the missing parts.
Saturate the areas covered in rust with a rust-penetrating oil and see what it takes to get the loose rust off. Seems more to be a case of powdery surface rust than any deeper corrosion, judging from the picture, and that should be easy enough to lift off without damaging the metal or any remaining original finish. When I say "see what it takes to get it off" it meens go easy. The toughest treatment should be an oily bronze-wool. Bronze is harder than the rust, but softer than the steel, so it will clean off the loose rust but leave the metal underneath intact. NO powertools should be used, no dremels or nothing. This is a job for your hands, oil and some mildly abrasive wool. If you´re not willing to do it right, then don´t do it at all.
I may sound harsh, but I can´t begin to tell you how many ruined antique guns I´ve seen. If you have to ask for advice here, you simply don´t have the knowledge to do a professional job on it. And even if you could do a professional job, the gun (judging from the picture) doesn´t need it. It just needs a bit of love and attention!
Anders Olsson