Since I assume you will be using Outlook App for your device (available for iOS and Android), this App is not counting against the number of installations you have for Office. You can download the App from iTunes / Google Play
Definately use the app instead of the URL although both will work. I think you will find that you like to having your mail on your phone if you approach it as a system. Everyone has their own preferences, but here are the strengths of each way of accessing you mail in my opinion.
Phone App: frequent monitoring of mail. While waiting for a meeting to start or standing in line at the store, you can quickly scroll through your recent mail to scan for important messages from clients or bosses. In addition, you can quickly swipe one direction to delete junk and the other direction to move to archive.
Outlook Desktop Program: creating mail and responding to mail. Some e-mail only requires a short yes, no or how about 3pm. Other mail requires a few well crafted sentences and a couple attachements. I still prefer to sit at a desk and type. In addition, the desktop program is great for sorting and searching.
Outlook.com: integration and collaboration. My personal favorite is to access my mail on my Surface through the web-app. This offers a full range of services like OneDrive and Flow. The biggest benefit is online, real-time collaboration with peers. Once employees start collaborating online through Office 365, you will start to recover all of the lost time caused by in-person meetings.