I have a scanner, Mac and old photos I want to scan. What's the best way to proceed?

The advice I got was “maximize your settings.” That is, maximize your resolution and size instead of accepting the scanner software’s default settings. You’ll probably have to play with the settings to get the results you want, but then you can scan away.

Your scanner probably came with some scanning software.
If you have Photoshop you can also ‘import’ through a scanner.

In either case what you want to set is the dots-per-inch, DPI, of the scan.

Note that “keep them at their original size” is meaningless, they will be files on your drive, they will show up on a computer screen at roughly 70–100 DPI, and if you print them that will probably be at either 300DPI or 600DPI. So you don’t capture any particular “size” when scanning. You capture at a resolution setting.

How you expect to use the pictures can guide you….
A lot of color printing is ok with 300 DPI.
But since you can always throw away resolution, and you cannot recover it from a lower-res scan, and you’re going to all the trouble, and you want to do this just once, ever, I suggest to give yourself a little future-proof room and scan at 600DPI or even 1200 DPI if the pictures have a lot of detail and the scanner will support it.

You can later use Photoshop or an app like it to output an image file that has the final resolution you need for your end use.

@dabbler is right. Increase the DPI to maximum for the highest resolution. You can get new images printed by uploading the digital files to a company like snapfish.com and printing them the same size they currently are.

If you have photoshop, you can make them look even nicer by getting rid of scratches, and correcting color balance issues. That’s what I usually do. :)