I forget where the numbers come from, but you've got it right. There are 5 worlds, each with their associated Nexus archstone, and then the worlds are divided into 4 or 5 consecutive sections by boss battles. I think there's an arbitrary force field in world 1 that keeps you from progressing until you've beat a certain number of other bosses, but otherwise you can pick and choose where to go next. I'd echo the general Souls advice of going on the path of least resistance. If 2-1's a pain, try 1-2 or 3-1 and see how they go.
Royal is considered to be a good newbie class because magic is pretty good against early enemies, and they start at level 1, allowing a bit more customization when you start statting up.