Double clicking on a .sit file normally launches Stuffit to expand the file. When I've installed OS 10 on a machine, the file association has been set by default.
That means that after downloading the file, it automatically activates Stuffit and you end up with the expanded file on your desktop.

If that is not happening, single click on a .sit file to highlight, then use the 'apple' and the letter 'i' (command i) to do a 'get info' for that file.

In the small window that opens for the file, use the pulldown menu and select 'open with'.

It should be set to Stuffit Expander. If not, make note of what it is and then change it to Stuffit Expander. If you see a checkbox that says "Change All" click on it and then close that window.

Now, you should be set to open all sit files with Stuffit.

If you run into zip files or others that need expanding, you can use the same procedure to set their associations.