Just bought a 1996 Grand Marquis LS 39,000 Original miles

Just bought this car a week ago from a elderly person. Car has 39,100 miles. The car hasn't really sat it just hasn't been driven a lot. I was just wondering what are some things I need to check/do to it since I'm trying to get everything tuned up on it. I just did a oil change, transmission flush, top off on all fluids, tire balance/rotation, and I'm going to change the spark plugs and maybe do a coolant flush this weekend. The car seems to run like brand new, everything works fine on it the only problem I've seen with it which isn't even nothing major is when I go to start it up for the first time of the day it seems to hesitate to start but WILL start with just turning the key over for half a second (Seems as if it wants you to tap on the gas or something for it to run but it doesn't require 2 cranks, just one).

Also is there any other things that I should be concerned of about this car? My first time owning a Mercury so I was just wondering. Seems to be a really nice car my first week of driving it.

There waas a class action suit on these cars (and many others) about the plastic intake manifolds cracking. Do a search on it and you will come up with many hits. If your manifold has not been replaced with the new style it will probably crack. Otherwise a good car.
http://www.usatoday.com/money/autos/2005-12-16-ford-manifolds_x.htm

I recently bought this 2001 LS with 25,000 miles on it. It had the original tires with most of the tread left but I had them all replaced due to the age and the cracking that was evident on the sidewalls. I would recommend that you do the same since yours would be at least 15 years old by now and not safe at all in my opinion.-Brian

Good advice on the tires...you don't want to be headed down the highway and have one dry rotted tire quit on you.

Sounds like you've done all the right things. Stay up on the oil changes and your Merc should last through 200k. I've owned 2 and both were over 150k with no issues when I donated them.