There is no right answer. It's up to you how you compromise, considering the following:

• 3840x2160 is the highest resolution for consumer displays. This is known as 4K Ultra-HD and is not widely adopted yet. If you are sending a landscape image at 3840 pixels wide or a portrait one at 2160 tall, nearly every one will be able to see full details that their screen can show. Since this is roughly 8 MP, sending an image of this size is the heaviest. Compressed slightly it should take 2 to 4 megabytes which most - if not all - modern email servers can handle.
• Consider 1366x768 to be a minimum. Looking at statistics gather last year from W3Schools, this was the most common resolution, used by 33% of people. 1920x1080 was used by 16%, while other high resolutions 32.7%. Other sources of statistics quote similar numbers. Note that this is the size of the entire screen. If you want to minimize the size of your email attachments, then use 1366 on the longest side for landscape and 768 for portrait.
• 1920x1080 is a safe resolution to ensure that most people will be able to see an image which is not blurred by interpolation. It is less heavy than 4K but the majority of displays have that or lower resolution. This is also a very common resolution for tablets and phones which many people use to read emails now. Ironically, as I am writing this, I realize that this does not apply to any of my displays since I have a 2560x1600 and a 3840x2160 display on my computer and a 2560x1440 on my laptop :)