A "sorta scout" can be done for not too much money this way (though there are some tradeoffs).
Use a .308 Remington 700 Youth Synthetic as the base gun. It has a 20" barrel and a short stock. Remington claims it at 6.75 pounds, though, so you may be pushing all-up weight. You can get these at Wal-Mart for $369, if you can stomach buying a gun there. Plan on $400 at your friendly local dealer, if you like to support real gun shops.
Natchez sells the Burris heavy-plex scout scope for $200. If you prefer the Leupold, get one for $220.
Get the B-Square scout mount (same one Savage used on their Scout) from Brownells for $29. While shopping there, also get a Williams WGRS rear aperture sight for $35. Plan on tossing out the screw-in fine aperture and just using the big hole as a ghost ring.
Order a Ching Sling from Andy Langlois, Galco or The Wilderness for $60.
Get swivels and an extra stud for $20. Installing the middle stud is no great trick for anyone possessing basic skill with tools. Also get low scope rings for $30.
The stock Remington trigger can be tuned a good crisp pull by a patient shooter. Good instructions can be found online. If you shy away from trigger work, pay a local gunsmith $50 to adjust the trigger.
Total for a functional, though not "slick," pseudo scout done this way (going the Wal-Mart/Burris route and doing your own trigger adjustment), is under $750 before shipping and taxes. Add extra bucks for buying at a gun shop, getting the Leupold, and/or paying a gunsmith for the trigger work. Optional extras, perhaps added later, are a buttcuff for spare rounds and a square post front sight.
Downsides are that the rifle may or may not make weight, has a blind magazine, and no bipod. But it'll be short, fast-handling, accurate, with a good trigger and scope, and backup irons.