The easiest way to handle this is to leave a copy of the message on the server for the laptop, which will allow you to download the emails on a designated PC.
In Outlook this setting is found in Accounts > Change > More Settings > Advanced tab.
As you have more than one PC you may need to use this setting on one of the PCs -just work out which PC will be the main repository.
But as you are not emptying the mailbox on your ISPs mailserver, you will need to watch out for full mailboxes if you have small mailbox space and high email volumes.
Another way to do it is to access your email via *webmail on your lappy. Nearly all ISPs have this but you will lose much of the functionality that Outlook provides.