I know that approach to buying a car all to well. I have flipped it upside down twice now.

The first time I found the car I wanted, and then passed the negotiating to a buyers agent. They got it from beyond my budget to a little under. They got a better price on the new car, while also getting a better price on my trade in.

The second time I went another way, I decided what features were important for me and then went looking for a car that fit the features and the budget. Technically, it went a little over my initial budget, but I was attempting to get a lot for much less than market rate. All up I was quite happy with the result in the end.