i've been a ford lincoln mercury tech for 20 years and i also like the LS. pretty reliable, nice looking, plenty of power.
here is what i have found to be the most reoccurring problems found with the LS.
The valve covers leak and will allow oil to leak outside the engine and also into the spark plug areas
which cause an engine misfire. have a mechanic check for this before buying vehicle.
the ignition coils sometimes go bad when this happens. the coils also can go bad if spark plug boots are worn. get as many maintenance receipts from previous owner as possible to see if tune up done. when you drive it, if the steering wheel shakes when you brake the front rotors are warped.
if you have to replace any coils use ford parts, aftermarket coils seem to be of lower quality.
The sensor/solenoid on the hydraulic fan pump sometimes fails. if engine starts to overheat have it checked immediately.
i have had to replace the solenoid valve body in transmission a couple of times but have only overhauled 1 transmission in the LS.
very few engine concerns other than valve cover gaskets.
Before you buy the vehicle have it inspected by a lincoln tech or a qualified tech with experience with the LS. you may be able to negotiate the cost of this inspection with the seller. have them check brakes, tires, valve cover gaskets, coolant quality, leaks etc... as anything wrong with the car will come out of your pocket later. do this with any car you buy! also since you're 15 (16) take someone older (no offense) Dad, Uncle etc.. with you so you dont get taken advantage of.
Think before you buy, look at several vehicles, dont make a rash decision like buying it because you like the stereo or its got cool wheels and overlook things like worn tires or brakes. i hope this helps. i would buy an LS if it was in good shape and well maintained.