My budget is under 15k.

If you don't care, then there is no reason to even think about getting a new car. You can get one with 7k miles on it that has been owned for 6 months for a significant reduction in cost.

Towards the end of a month, and towards the end of a current model year (when buying new).

I don't really care too much about brand.

Your loss.

My car is 11 years old and has 165k miles on it. My wife's car is 16 years old and has 139k on it. Needless to say, either one can go at any moment. With my last grad school payment to be made in May, I am looking to start using my extra income toward the purchase of a car.

So when is it the best time to get a good deal on new car or slightly used car? I don't really care too much about brand and style. Just want something that will get me two point A and point B with good gas mileage and wont break down. My budget is under 15k.

If you don't care, then there is no reason to even think about getting a new car. You can get one with 7k miles on it that has been owned for 6 months for a significant reduction in cost.

It's always better to own your car outright rather than to get a loan on it.

Some time in the summer all the car companies will release major incentives to get rid of inventory for the next model year which starts in the fall. By doing that, you save enough to make the difference between buying a used car in the same model year and a new car without dealing with the issues of buying a car secondhand and the added wear and tear and mileage.

I usually wait for a natural disaster. That's when Toyota offers the best deals.

Not true.

There are many situations where its better to have a loan. For credit purposes etc.

Thorough research has shown that 100% of cars repo'd had a loan owed against them.

Not true.

There are many situations where its better to have a loan. For credit purposes etc.

A car decreases in value the longer you drive it. A new car is $200 or $300 a month plus expensive car insurance and you pay a lot in tax to the DMV to register the car. If you have a nice car like that you're probably in trouble if you get in a car accident with someone with little or no insurance. You absolutely have to get the car fixed if it's not totaled. As long as you don't buy a lemon your used car repair bills will likely be cheaper than a car payment.

You're a college professor, shouldn't you be riding a bicycle to your tree-hugger meetings or riding in an early-70's British sports car?

I am not a college professor. I teach Junior High kids.