Given a .22 has a limited "long range," something like a Mueller APV (around $130) should work. It's a 4.5-14x 40mmAO and works well for ranges that a .22 can reach. It's not extremely high quality glass, but it is very clear from edge to edge and focuses very well. I like mine.
Using Burris rings and maybe Weaver bases (what else can you use for a Savage?) that'll get your scope cost up to $160-170.
If you have a lathe or have a friend that owns one, or are on good terms with a machine shop, you could get ahold of a 10/22 aftermarket barrel and have them lathe down the barrel shank to fit the Savage reciever. Doing it with a lower cost barrel like a Green Mountain could keep you below your price limit, and if you did it with a sporter weight barrel you could keep the rifle light and have it shooting well.
I basically did that with my Marlin 980S and saved alot of money by doing all of the custom stock work and bedding myself. It shoots extremely well and you'll be saving money by using a Savage 'cause the Accu-trigger will work well. I replaced the T-900 trigger with a Rifle Basix that I got barely used but works very well.