Vista - Converting Webmail to Outlook - Help!

I've been using my company's webmail account for several years and now they are switching their webhost. For email, I am using our hosting company’s webmail system (IceWarp Web Mail 5.6.7 - IceWarp eMail Server Software).

The webmail program is basic, but it works, and I now have about 4 years of emails on it – so it runs very slow.

My other business partners use POP3 – Outlook for their email, but they go into the office everyday – I work from home and travel a lot – which is why I was using the webmail.

Now, we are going to switch hosts, and before that happens, I need to get all my webmail off the current host’s server – and get it into Outlook.

I actually need something like this:

1) Emails that are stored on current host’s servers – are organized and ready to be removed from the servers.

2) I would prefer that the email is put into my Base machine, but I would like the ability to back-up/clone the Base outlook account – and transfer that file to another machine, so on the road I can still access old email.

My question is, how would I go about doing this?

Can outlook do this? Or do I need a different email client?