Art Board Size Selection

While vectors can be scaled/printed at any size, the size you make them (and the size of the arboard) does tell someone what size you intend them to be used at.

For example, if you make an illustration on a postcard sized artboard, that's the size it would be when you import it into InDesign. While they could scale it up/down with no loss of quality, it starts at the size you made it in Illustrator. 

Also, if you want to make something 2in x 3in, building it at the correct size will let you make things an exact size using the Transform controls or when you click to make a precise shape (as opposed to dragging to make the shape).

One more example, if you're creating art that will be animated, it's ideal to create it at the same size as the final video (1920x1080 for HD for instance) so that when you bring it into After Effects, the compositions that are created will be the proper size.

In summary, working at the correct size is a best practice... but if you don't make it at the correct size, vectors will allow it to be fixed without loss of quality (but it does create more work).

I hope that helps.

If you create vector cartoons, they will be scalable to any size.

But if you know at what size they will print, make that print size the size of your artboards.