my MACBOOK PRO can not install the Updates du to missing the digital signature on the software, can anyone help me please

Which update? Where did it come from? Most likely, corrupt, so delete and redownload another copy.

Wondering how to download from update site? I have 10.6.8 and need to upgrade, do I jump to the most recent version, or to 10.7?

Also, if the automatic update doesn't work, what do I do to use something from the download site?

Which updates? Upgrading indicates you want to go to Lion or later. Be specific.