What's the best size for a graphic with text sent by email?

A lot of the good information on this topic comes from websites that advise in best practices for email campaigns, because the goal of those campaigns is to get those messages opened and read. Below are a couple of articles found on a Google search.

Learn the best image width and sizes for your email campaigns | Campaign Monitor

Email Maximum Width: Still 600px? > Litmus

72 dpi doesn't apply because displays now range from 96 ppi to well over 300 ppi, from large desktops down to smartphones. What matters are the pixel dimensions—how many pixels wide and tall. The consensus seems to be that 600px wide is a good number, but some emails are designed to look OK at 960px or over 1200px wide depending on the expected audience.

72 DPI is common for web graphics, but the best or optimum depends on the user's display.  If they have a retina display or greater images or graphics can be larger.  Remember there is a 20mb limit on email size so keep the total size of your email under that.