I want to create a link / button on my homepage that takes the user to a specific form to edit the only record that user has access to in a table.

You could do this by creating buttons as formula URL or formula text field in the table in question. Then create a report that only contains the button fields. Since a user is only able to see their own record, then this report should only contain one record/row. Now you can use this report on the dashboard.

Now for the specific form and edit vs view. You can craft the URL in the following way in the formula

URLRoot() & "/db" & dbid() & "?a=dr&rid=" & [Record ID#] & "&dfid=10"

dr is used for view and er is used for edit

dfid is used to select the form you want to use

I know this solution is not the most elegant but is will work.