$1800 is WAY TO MUCH!!!
My first car was a 85 Firebird. The motor is very weak. I stroked and bored mine and got some good power, and also made it handle like its was on rails, but move on.
On don't get a V-6 and think yu can just mate a V8 to the trans and go. The Trans on the V6 is made for the V6. The V6 is a 60 degree Metric motor, the V8 is 90 degree and Standard, i.e. will not work.
I am a mechanic and can tell you don't look at a v6 F-body until 1990. And don't look at a V8 until 1988. If you get a older 82-92 F-Body get it cheap and with a Manual Trans. That way you can dump any engine in it and with the manual Trans you don't have to worry about the computer messing with the auto trans.
Most, NOT ALL, GM cars from 79-86 are not good. Even the Corvette had its growing pains in these years. And I say this as a person that has a 75 Chevy Monza.
GM makes the best cars in the world bang for your buck, but that is NOW not in 79-86.
Good Luck