Accessing roadrunner mail away from home


New Email
I use time warner roadrunner in Austin, Texas.
I have Microsoft Outlook setup on my home computer.
I have an apple smartphone.
I would like to be able to access my email when I travel. Ideally would like to see any messages I have left in my inbox, not necessarily those I have filed away in my personal .pst files. Althought that would be a bonus.

The problem is that with POP3 the messages are moved to my home computer as soon as they appear in the inbox.

I have modified the settings in outlook to leave messages on the server until I delete them, but after a while found that my roadrunner inbox was full. When I went to the web interface I found tons of email that I had deleted or moved to a local folder on my computer still sitting on the server. That took me several minutes to clean up. And was confusing to determine which messages I had removed and which were new or ones I wanted to keep.

The only threads I can find on this kind of problem out there are dated - about 4-5 years old. I am thinking people have solved this problem, and I'd like to know... is there an answer? Is there a way for me to use outlook on my home computer yet still be able to access my email from my phone or from the web on a remote computer when I travel?