I don't believe I've ever heard of any one using a bolt-action rifle for home defense, on purpose anyway.
Honestly, it strikes me that your goals are at odds with one another.
Cheap and long distance target don't usually go together very well, unless you don't particularly care how big your target has to be to hit it.
Sure, you can shoot 4 foot square plates at 1000 yards with a Mosin (maybe) but that doesn't really equate to "target" shooting for most folks. If you're talking about shooting small groups, you need a decent gun. Decent guns aren't usually "cheap" to the same degree as old/surplus military.
Still happily answering to the call-sign Peetza.
The problem, as you so eloquently put it, is choice.
He is no fool who gives what he can not keep to gain what he can not lose.
-Jim Eliott, paraphrasing Philip Henry.