There's usually a couple of groves in the base which you can use to guide the paper, ...
Yes. There must be some "groove" or other mechanical thing to guide/facilitate the placement of the paper. If not, it would be difficult, at best, to get the paper where one wanted.
But, assuming there is not, you can make your own placement guides with tape.
I use (even with quality easels) gridded paper for setting up. This facilitates two things: If cropping the negative, I get the proper alignment of the image on the paper, i.e., making sure something is (or is not) centered, or the horizon straight, or whatever. (Obviously, if one prints the entire negative, especially with the rebate showing, this is moot.)
The other thing I use the gridded paper for is to set the blades for the margins I want. I find this method - even on a Saunders or Kostiner easel - to be much more precise than using the scales on the easel itself.
So, look for the device on your easel for positioning the paper. If there is not one: take a piece of paper and draw lines on it for the margins you want, and use this to set the blades where you want them. Then use that paper still in place to put some tape on the base of the easel to show where the printing paper goes. That should do it.