Congrats!
I also have a 2001 LS. It is a V8-Sport 49k miles/Black/Tan/w the chrome rims. I really love this car and you will also!
What color is yours and how many miles does it have?
This is what seems to be working for me....
Wax - I'm still experimenting. If it is a dark color like mine, stay away from the polymers. I was satisfied with using P21S Cleaner and the Meguiars Gold Class Polish (made it look really deep black and wet..nice) but am going to try PoorBoys w/Carnuba to see if I can cut out the cleaner step.
Seats/Steering wheel/Interior/Doors - 4STAR Leather Cleaner and Conditioner....and...*gasp* Every so often I'll use Formula 2001 on the dash

Chrome Rims - WheelWax
Wheels - Meguiars Endurance (Natural)
Trim - Meguiars Gold Class Trim Detailer
In between washes I use PoorBoys Spray & Wash and 4STAR Ultimate Gloss Enhancer.
BTW: If your looking to do some upgrades or just have general questions about maintaining the car check out the LS Owners Club
http://www.llsoc.com It costs $35 a year but there is a free trial membership so you can look around. It has saved me about $400 in parts and alot of headache when dealing with Lincoln/Ford Service Departments by knowing exactly what to demand/ask for and how they deal with certain situations.
-Kris