Not slim pickings at all between the plethora of budget rifles available today.
My first choice would be a Gen 1 Ruger American .223 rotary magazine. Ranch for a 16" barrel or Predator for a 22" pipe.
6lbs before scope, 6rds in the loaded mag and one hand carry with the flush fit of the rotary. Decent enough profile on the barrel, not a pencil. Good balance on the Predator model, overall a fantastic walking Varminter.
Folks will crap on them but with the amount of time the rifle has been in production and the sheer number of them in field use it is becoming undeniable that they run trouble free and shoot MOA.
I have a Ranch that is coming-up to 4000 rounds without a hiccup, it happens to be one of my smoothest bolts to run from the shoulder as well, and I have custom bolt actions that cost five times what that one does to compare it to.