Email systems do not like large attachments, regardless of the file types.
The size to send will depend on what the receiver is going to do with the pictures. If the goal is to just view them, 2000 pixels on the long side is plenty big for most viewing. Printing often wants to have the full size images.
If you are sending images in large qualities or frequently, you may be better off using a photo hosting site, where you can upload the images once and let the site worry about what size to send to the viewer.