Update [07/22/2014]: 

You can choose which friends show up on your page by marking the ones you want displayed as a 'Top Friend'. To do this, view your friends list by clicking "See all friends" on your homepage, or by clicking "Friends" on the top menu bar. You can then select/deselect Top Friends by clicking on the star at the top left of their WeeMee (Top Friends are the ones you have starred).

By default, WeeMees are automatically added to your top friends as they're added to your friends list. You can disable this under Settings > Friends.

Credit goes to TheOtherBella for this information! Go give her hugs.

You cannot choose which friends are shown on your homepage (usually the ones that are currently online are shown). However, you can choose which friends are shown in your Room.

- How to: Add Friends to Your Room