The welcome email we're receiving from new member signups has the logo image way too large (See attached screenshots)

 

Where exactly in the admin portal do I go to adjust this? Also what is the proper dimensions I should have set on the logo for it to display properly in the emails..

There is no specific size, as it would very much depend on the browser its opened in. I Would say however, you should upload something much much smaller than what you have in Systemn->Settings->Email, as at present its clearly too large and is only used on email from that section. Other than that, please check you havent edited any email templates. I suspect that may be what is causing your issues there