If i am making a search from a list of fulfillment records, what would the join record for the invoice / cash sale reference be named. paid transaction fields, billing transaction fields, paying transaction fields etc..?

invoices/payments are not tied to fulfillments, they are tied to the sales order that the fulfillment was made from

My end goal is which shipping person fulfilled the transaction and the transaction total on cash sale or invoice

It depends how many joins you need to go and if you are using search or query/analytics. Just add the applying transaction/applied to transaction joins to your search, and you will see the relationships

72893 in suiteanswers is helpful as well.

do join fields only work with main line = false? I cant get trans # to pull up when it's true from a sales order using fulfilling trans number or applying transaction field using transaction #

Applying and Applied To are opposite directions, play with both until it starts making sense to you. You can also get the Link Type which will make it clearer.

Got it almost all sorted now, just having an issue with finding the right field to use on the invoice when not using main line to sum up the correct transaction total. sum of amount seems to double the value of the invoice for some reason