The on board FMP help index walks you through this, actually. Look at the topic "Editing Record Access Privileges". There's a bunch of info at the top, then the example you are asking about down below.
In your case, have the Admin use a layout where the "Account responsible" field is modifiable and have your operators use a layout where it is NOT modifiable.
Also, set the "Account responsible" field to autoenter upon creation Get(AccountName). For an Admin, it will autoenter "Admin" and then be changed by the admin via your dropdown. For a user, it will autoenter the account name of the person entering it.
If it is not necessary for your users to see the "Account responsible" field, simply leave it off of thier layout altogether.
Note that "Show all records" will show ALL records, and have the ones that they don't have privileges for blanked out. I tend to put a "Show All" button on the layout that actually performs a find for thier account name in the "Account responsible" field. At the very least, put a "Find Mine" button out there...the blank appearing records get annoying very quickly.
Thanks for the response Ninja. I gave some of the posts a quick glance and it seems to be what I am looking for. I will give you a definite answer later. Thanks again