well savage makes great rifles for the money but you are dreaming if you think you are going to me COMPETITIVE at 1000 yards with a $500 off the shelf rifle.
first define your type of competition..specifics. f class, bench rest ?? what ?
(your budget maker is in a dream world, not the real world)
savage top end rifles $1200-1600 will do the job....then add scope and other equipment.
quick break down of a 600/1000 yard br rifle : bbl 350( blank) chambered $125-150, stock 500-1000( mine was 770)
action 1000 to 1500 mine was 1400, trigger 200-500 base 100 rings 100, scope 1500-3500 mine was 2600 fitting and bedding( called a stocker) 500 or more.
over $4000 for a custom