The '58 remington is the pistol I would always suggest a new buyer to purchase. The cylinder can be taken out very easily. It is in fact designed for a quick change to other loaded cylinders. Colts require you to use a hammer and punch to knock out a wedge and pull the barrel off if you want to change the cylinder.
The caliber is where things get a bit odd. The one you have is .36 caliber, meaning that it is a Remington New Model Navy 1858. The normal Remington is a .44 caliber, the caliber the US army used. The navy used .36 caliber.
As for shooting supplies, you will need a screwdriver that fits the screws to be able to dissassmeble the pistol. The revolvers get the fouling inside the action, so you will need to take the trigger, cylinder stop, and cylinder advancing arms out of the frame and clean them too. Also pull the cones out of the back of the cylinder.
The bullets will be oversized for the pistol, unlike muskets that use undersized bulllets and patches. No patches are used in revolvers. There will be a ring of lead shaved off the bullet as you seat it directly over the powder charge (normally a powder charge is 30 grains or so).
Another supply is Crisco, the cooking greese. You cover the front of the chambers with it to keep the pistol from chain firing more than one chamber at a time from the flames crossing the front of the other five chambers. I will add that there is some discussion that the bullets make a sufficient seal (remember the lead is shaved off when it is seated, so it should be tight). There is another reason to use the Crisco anyway, because it mixes with the gunpowder residue and keeps it soft enough to clean easily.