Not much really ... Caps, ball the right caliber size and powder. You might also get the lubed wonder wads in your pistol caliber to put between the powder and ball. Then bang away !!
If you are getting a .44, you will want .451 round ball. If you are getting a .36, then you want .375 round ball.
Id get a nipple wrench and a pistol cleaning rod as well. There are a lot of things worth their weight in gold for convenience, and you will probably figure out what those are for you personally after a few shootings. Also some oil like ballistol or rem oil is a good idea. After a few cylinders these guns can get really hard to turn. A little spritz if needed on the cylinder will keep you in action.
Caps- 10’s or 11’s. Can’t be choosy these days. Balls- I like .454’s for a .44 and .380’s for a .36 Uberti and .375’s for a .36 Pietta. Nipple wrench. Appropriate size wads is you want, but not necessary. Over ball lube if you want, but not necessary. An adjustable powder measure and / or fixed measures. Spring loaded capper is nice if you can find the caps. Powder flask or horn to keep your powder in. SlixShot nipples for whatever you buy. Proper turn screws for disassembly and assembly. Nipple pick. Cleaning rod, jag, brush, & swab. Lubricant of your choice. Honing stones to polish your internals. Dawn dish soap and cotton rags for cleaning. And a holster.