I just now (like 35 min. ago) handled one of the New England Arms Handi-Rifles, and they're really neat! They also will factory-install a new barrel for you for about $100!
They come with sights, and are tapped for scope mounts. One of the one I looked at had a Picitinny Rail on it, with open sights. They guy at the shop did caution that they're tough to take apart and put back together, though; press pins instead of screws. If I was REALLY on a budget, I'd look into one of those, and take my savings to a really good scope to put on it. Butt cuff, of course, would be mandatory...
Winchester was offering a package rifle for awhile at the Wally World (ugh). $420 for an M-70 blued composite topped with a 3X9X28mm Simmons sccope.