Excellent question. The official answer is Internet Explorer 11. Extensive testing however, shows the current Google Chrome works pretty much flawlessly for the email system as well. Firefox, Safari, and various other browsers have been very poor.
If you have an older PC running Windows XP (or Vista) you are not going to have the best email experience with IE, because your browser is old. Google chrome will still perform well on most of those systems but not all.
If you don’t have Chrome and would like it you can download it here:
http://google.com/chrome, choose download from the top. As with any download, read the dialogues that appear and uncheck extra junk (like making yahoo your start page, or adding the ask toolbar)