Outlook Web App is a fantastic web-based email client for Exchange Online. It's almost as full-featured as the desktop version, allows offline mail access, and provides a high level of customization.
It is, however, somewhat bandwidth-hungry. To help with this issue, and also address older browser needs and provide some accessibility features, the full-featured version of OWA can be switched to a 'light-weight' classic version of OWA. To do so, follow these steps:
Sign in to OWA, and click on the settings gear in the upper right to get to the menu. Then click on Options:
In the Options screen, click on General and then Outlook on the web version:
Now check the Use the light version of Outlook on the web, and then click on SAVE:
Note that you will need to sign out and sign back in to see your changes. To sign out, click on the icon/avatar (or picture, if you've set one!) in the upper right of the browser, and choose "Sign out".