Best way to get a few AA miles?

I am trying to book a flight, it'll be the first time I book using miles. I have 187750 miles, and the flight I'm trying to book is 188000 miles. 250 short. I will probably stop using that credit card afterwards, as I don't use it much to begin with.

Does that basically mean if I buy something with that card for $250 (or $125 if i get 2x miles, like for gas) that I'll get those miles? How quick do the miles show up in the account?

I remember hearing something about being able to buy miles, is there a minimum amount of miles we can buy?

Thanks for any thoughts and tips.