I'm also looking for a used car in the midst of the car shortage. While nereo's link has some good general car hunting tips, it's such a bizarre time to be a buyer. I've never used carvana or carmax, but I have used plain old cars.com successfully before and that's my plan now.
Last time I bought a used car I essentially haunted that site for a month, and whenever a car that fit my criteria/budget popped up at a dealer nearby I would zip down and check it out asap. As much as I hate dealerships, there is a big difference between walking in with an attitude of "what do you have to sell me" vs "I saw you have this specific used car online, x years old, with x mileage, for x price, can I see it/test drive it, and no I'm not interested in your other cars." I ended up saying no 3 or 4 cars before finding one that was exactly what I needed for a decent price.
Maybe someday I'll have the energy and guts to buy from a private seller/craigslist ad/whatever, but this is not that day.