Buy the frame first, then make the print the right size to fit it. You can even take the frame into the darkroom and project the negative right on it, size, and there you go.
We recently got some frames from Michael's. They were such garbage we couldn't use them. Fortunately, they took them back. They weren't wood at all, just plastic. Horrible! - but all they had. Check other craft stores. Fairly decent standardized wood frames aren't hard to find. If you don't quite like the color, shoe polish might correct it.
About placement in the matte. It won't work right if the print is off center from side to side. It also won't look right if the print is ON center from top to bottom. It baffles me why people have formulas or rules about how much more space to leave below the print. The whole thing about placement is proportion. For example, if you were to matte your prints leaving the lower part of the matte 1/2 inch more than the top, or anything like that, it would be very different if you were matting a 2x3 inch print on a 5x7 inch board, than if you were matting a 2x3 FOOT print on a 5x7 foot board. In the first case, the 1/2 inch might be too much. In the second, the 1/2 inch would have no visible effect. Vertical placement is best determined by simply looking at it and finding where it looks right. Side to side placement must be measured carefully.
One very quick and easy way of centering the print side to side if you are dry mounting with the margins trimmed off is to move the print to one edge of the board, so that the edge of the print corresponds with the edge of the board, then take a strip of paper and with it, measure the difference from the other edge of the print to the other side of the board, marking the strip with a fingernail. Then, fold the strip of paper from the end to the mark. What you've just done is to determine without a ruler the difference in size between the print and the board, then divided that difference in half. Then you can use the strip you've made to set the distance of the print from the edge on either side at the top and bottom of the side of the print.
Then all you have to do is visually set the vertical position, tack it, and you are ready to press. It is incredibly easy. You've done it with no abstract math. I hope I've explained it well enough. Using this method, you can probably matte 4 prints in the time it used to take to matte just one.
Unfortunately I know of no similar trick for laying out the overmatte. Wish I did!
Cutting: I learned to cut mattes with a Dexter when I worked in a color lab back in the 1960's. Professional framers laugh when I tell them that, but the fact is, you actually can cut good mattes with it, as unlikely as it seems. Subsequently, I bit the bullet and bought a second hand C&H professional cutter. It's great, but I still mess up now and then, and with good museum board, that's distressing.