How do I select what record type I want to make an Advanced PDF of? I select New Template from the Advanced PDF / HTML Templates and It only lets me make Saved Search Type PDFs

You need to go on the standard PDF template of the record type you want to create. then Edit it. once you save it it will automatically create a Custom Template for that record Type

No need to select record type here. Once you done with Template creation, go to the record you wish to set that template and go to customize form then got print template drop down field and select your template and hit save