This is my first car, I was browsing on carmax.com and fell inlove when I seen this little black 2 door Car, I have a daughter so I don’t want the car to break down with my daughter possibly being inside, these were the sellers notes “2002 cougar.sporty.fun.economical, this car looks,runs,and drives great and is loaded with options.very clean inside and out.super smooth v6. these cars are getting harder to fine that are this nice…” I really think this is the most adorable car I’ve seen but should I purchase it with that many miles, I only work, or want to take her to daycare, and occasionally go out on weekends, do anyone think this will be a good buy??..
Depending on the age of your daughter, you may want to reconsider the idea of any two door car altogether. As in, if she’s still young enough that you will have to be putting her in a car seat, buckling her in, unbuckling her, and lifting her back out, you want a four door car more than you know.
As for the car itself, this doesn’t sound like a bad price to me if the car is actually as described. I just would not want to have it and a child in a car seat at the same time.
If it is the base model and in clean condition (slight but normal wear), then it is priced about right. It’s hard to tell without additional information. What model Cougar (base, sport, sport premium, or sport ultimate)? What options? Is there anything wrong with the car? You may need to have a prepurchase inspection to determine this. Any repairs needed are deducted from the asking price. If you like it after driving it and giving it a good look yourself, pay around $100 for a prepurchase inspection.
For a 2002 car that mileage is about right. It is a 10+ year old car now, so you have to expect some repairs and put some money for repairs in your budget.
If you have a car breakdown you need a contingency plan, such as a AAA membership, a cell phone, and the phone number for a taxi if needed. Even brand new cars can breakdown, so there are no guarantees with any car.
With an older car you minimize on the road breakdowns with good tires, replacing old heater and radiator hoses, and replacing the serpentine drive belt every 5 years. These are common items that fail at the worst times. Other than that, you just take your chances like everyone else.
As a mechanic, my input is that the Cougar is a different breed of car from other Ford/Mercury products. I wouldn’t say they’re particularly unreliable, but they’re harder (read:more expensive) to work on than other Ford cars of that era, and many parts are unique to the Cougar, meaning more difficulty for repairs in the future.
On the other hand, if a car isn’t fun for you to drive why buy it? $2500 is nothing for a decent running car these days. Put a little aside for the unexpected and have fun.
If it passes your independent mechanic’s inspection then it’s not a bad deal at all.
These cars are based on the Ford Contour/Mercury Mystique platform. That’s not a bad thing, in and of itself, but all of these cars have been out of production for a while, so could parts availability be an issue? Yes, if you’re talking any used parts. As Mark said, a 4 door would be a more practical and safer choice for your daughter. However, your choice of a screen name suggests you’re looking for something a bit less pedestrian than a Taurus sedan. 
Some cars with only 40k miles on them are ready for the crusher so mileage is not always the main factor in a car purchase decision. A thorough inspection should be done before considering buying the car and keep in mind that even the finest of inspections does not guarantee you a problem-free car. It helps to swing the odds into your favor a bit is all.
You should also not allow certain feelings such falling in love with it, thinking the car is adorable, and so on to cloud your decision.
Sitting on the side of the road in a cloud of steam or with a fried transmission could easily make love and adorable go away very quickly.
JMHO, but I’ve always considered that era of Cougar the orphan child of Ford Motor Company. Basic maintenance and wear and tear repair parts can be found but a number of repair parts could turn out to be “dealer only” and that can sometimes translate to good luck.
Given that Carmax is selling the car says something good about the car itself, but I still don’t believe in buying cars of any age with more than 100K miles for someone with very limited or no mechanical knowledge about that particular car.
IMO, you should buy a car with less miles, there are so many new cars out there with good prices, long warranties, and great financing arrangements you should seriously consider them.
I would not be surprised if you spend another $1500 or more over the following year on the repair or replacement of parts that are due for replacement. Those costs just keep adding up they only stop when you get rid of the car. That’s why I always recommend the purchase of cars with warranties.
Hyandi was one of the first car companies with a 10 year bumper to bumper warranty, now many car makers have long warranties like that. .
@LetsPlayArmis a colleague recently bought a car from CarMax. It turned out to be a POS. The MIL came on, due to misfires. It turns out there was a TSB that instructed you to repair the valvetrain. When he confronted them, they told him they had hoped it would hold out long enough for him to not be able to return it.
They admitted that they knew the car had a problem. They even knew about the TSB. They admitted to clearing some codes (before he bought it), hoping that the problem wouldn’t reoccur. And the price, while fair, wasn’t great.
So he picked out another car.
My point is that you need to be careful with every car you’re looking at. Even the big guys will occasionally act shady.