I really like avast so far, best AV I’ve ever used. Which provider should I use to secure my Outlook Express mailbox - the internet mail, or the outlook/exchange?
Welcome to the forum! 
You should use the Internet Mail provider for your Outlook Express mail.
The Outlook/Exchange provider is for Microsoft Outlook, and NOT for Outlook Express. They have almost the same name, but they are different programs.
I suggest a browse of the avast help file to get familiar with avast.
Stick around and browse the forums, especially the sticky topics at the top of each of the forums. They provide a wealth of information to help you get the best from avast.
Welcome to the forums.