Personally, I would go to either Berks, Bucks, or Lancaster Co.
I went to Berks. The reason: Chester Co will not issue to people from
out of State. If you go to Media, it will require 2 trips. The 3
counties listed above will issue on the spot (20-30 minutes) and will
cost you $20.00.
Go anytime between now and the expr date of your current LTCF.
I'd take a copy of my DE drivers license and DECCDW. You can go to
http://www.pafoa.org/counties select the county you are
interested in going to and go to that counties sheriff’s web page for the
application and instructions.