Hi Dan. What you want to achieve sounds very reasonable. If I understand you correctly, you want to have links on the default page of a SharePoint Online site collection that when clicked, will open up a new browser window and navigate the user to say, a subsite within your SharePoint Online site collection or even a site external to SharePoint Online?
If that is the case, then there are a number of ways to achieve that. Here is one suggestion:
Use the Site Actions menu to edit the page add add in a content editor web part. Modify the new web part and select the Rich Text Editor button from the right hand tool panel. Use the hyperlink button to add in a new link: enter the URL but make sure you check the box "Open Link In New Window".
Click OK to save the changes.
When a user clicks your link a new browser window will popup and redirect them to the link you have specified.
Hope this helps.
Regards,
Myles
http://twitter.com/mjthinkscape