What is the ideal size for tile images?

You need tiles with the same or bigger size as the size of tiles in your printed mosaic. If tiles in your printed mosaic will be 1 x 1 inch and you will print it at 300DPI - you need your tiles to be no less than 300 x 300 pixels. You may use bigger tiles 400 x 400 or even 2000 x 2000 but not less than 300 x 300.

You may just use large original 5 - 10 - 20 Megapixels photos. It will takes a little longer time to save output mosaic in this case but - IMHO - there should be not very long.

Indeed, you may downsample a very large photos to some middle sizes like 640x480 or even 300 x 300, usually it is not necessary but in case of very large libraries and mosaics it may speed up the process.

Also you may prepare a cropped photos: cut one large photo into few smaller different pictures. It's good to get a large number of different tiles. See here for more info.

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