A bore sight just gets you on paper without wasting ammo but 22, even match 22 is cheap.
As for scopes I strongly recommend investing in good quality scopes and you won't find one for less than $100. You'll also want to match the scope with intended use and for a hunting/plinking rifle a fixed 4x like a Weaver RV4 4x28 rimfire
scope or a variable power RV7 2.5-7x28 rimfire
scope are excellent choices. Both offer good glass and rugged construction that should last you a lifetime. If your interests run more to target shooting than hunting then a Mueller APV 4.5-14x40 is a decent if light duty scope to get started in target shooting for cheap (~$130) but the crosshairs are a tad thick.