PDF Form -- Options?

I am helping a church take their new member form (PDF) and putting it online. We are looking for the form to be available for new members to complete via a link from our web site, and then for a copy of the completed PDF document to be e-mailed to a list of recipients for processing. Ideally, it would also save the results into a Google Spreadsheet so others can access the raw data electronically.

Is this something G Suite can do? Searching points to a lot of pay per month options like DocuSign and Adobe Acrobat Pro. We are trying to use GSuite if possible to keep costs down (we already pay for it).

Any direction would be greatly appreciated.