Hi,
You DO know this baby project is a KIT, don't you? It comes with 14 count aida and will be 10" x 13" when complete.

If you decide you want to buy the kit and change out to a different fabric, you can do that and then decide what size you want the pattern to be. I'm prejudice when it comes to type of fabrics to use since the majority of my stitching is done on 28 count evenweave fabric. I use this fabric because each square is equal in size and I also like the finer background the higher fabric provide (where you don't see each individual square when you're up-close). But it is YOUR project, it's important that you decide what type of materials you would like to use so you ENJOY doing it...:)

Can the Aida be substituted with linen? And what size?

Read Bermuda's reply again. Comes with Aida.

If you want to use a higher count of fabric, rather than use the aida material that comes with the kit, you could use a 28-ciount EVENWEAVE ie. Jobelan to keep the finished pattern as the same size as the 14 count aida. BUT on the 28-count you would stitch OVER 2 Squares on the evenweave as compared to stitching over one square on the aida to keep the dimensions of the finished project the same.
I add 3 inches to each side when calculating my fabric to allow plenty of material for mounting and framing..