I test drove a used Lincoln LS today and I am very pleased. Its a 2002 model and it extremely clean with very low miles. I am a single mom and I am in need of a 4 door car. Im just very weary about investments of this amount. Any suggestions/complaints of what I need to think about on the LS? I have always drove Ford or Pontiac. This is a (I feel) a step in the right direction for me on a used car.

Welcome to the board.
Before you buy, if you buy, inquire about if the...
Solenoid packing has been replaced
Valve body has been replaced
Coils
Tie rod

Do a search and you'll find a lot of common issues that you'll pay for if not already installed.

does it have a warranty, if not purchase an extended, around $1000-1200. Drive it gentle, take care of it and it should last you a while. Definitely inquire as to what has been done to the car in the past. Not sure of your financial situation but you need premium gas and repairs are relatively expensive. i have no complaints about my car, would not change a thing. use your best judgement....

if you get an extended warranty, you should be okay. I say this for a couple reasons...

The LS has a few trouble spots as KD00LS said, but I'll add to that:
window regulators (controls the windows going up and down) (first Gen)
Ball joints (suspension) (mostly first Gen)
Hydraulic cooling fan (engine-cooling) (First Gen)
Valve cover gaskets (engine) (00-mid 03)
PVC Hose on V6 (engine) (all years)

And the things KD00LS said:
Solenoid packing has been replaced (transmission) (first Gen)
Valve body has been replaced (transmission) (first Gen)
Coils (engine-ignition) (all years, but accelerated by valve cover gasket problems)
Tie rod (steering-suspension) (all years)

These are not areas you WILL have a problem with, they are just areas that have what most of us would say a more frequent occurrence of problems across the board than most other vehicles. There are a lot of owners who never have a lick of trouble, then there are a few that have all of them. Most of us experience one or two issues. It is to be noted that second generation cars have fewer of these problems, but some are shared. First generation cars are 00-02, second are 03-06.

If ultimate reliability is your goal, Honda, Nissan or Toyota would be your best bet. But that isn't to say the LS is horrible, just be aware that it takes a bit of maintenance.

Another thing I see you previously had a Pontiac. If it was a Grand Prix you might notice there is not as much room in the rear seats. That's how I felt anyways when I switched over.