Howard is quite right, you cannot filter categories. There is an easy way to sort the front page though with a few tricks in the Front Page Settings page...
1. Switch all options to "None"
2. The checkbox "Include Topic Section" is checked.
3. Save the changes.
Return to the Front Page and turn editing on
The central panel should be empty, so select Add a Resource and add a label.
In the label you can place a table with images as shown in the link above, use your own images of course. If you don't want to use images, use text, but you need some visual cue to encourage new users to explore, and as prompts for existing users who know where they are going.
To find the URLs, as Howard says, they are fixed, so before turning them off go to each one, then copy the URL in the browser address bar. Paste it to a text file, or if you have created your Categories sequentially, then all you need do is to change the id number of each Category. Do not list any category you don't want publicly displayed.
For me, text links are boring, images provide colour and can offer some excitement. The modern trend is toward corporate bland, a dreadfully tasteless set of grey images at best, you only have to look at the Atto toolbar to see what I mean. They may be functional but they are no fun.