Savage/Stevens is awesome, and a Stevens 200 in .223 runs about $300. No irons, though. Couple hundred towards scope, base and rings, and you would have a rifle that may very well shoot ragged little holes. If you lost your mind and decided you wanted to go hunting with Texashiker, you could easily swap calibers with some pretty basic tools and parts. The great thing about the Savage/Stevens platform is that you don't need to do any chamber reaming to set headspace during a barrel swap.
You could do a Savage .22 for a couple hundred, and buy a shitload of ammo, but most of your shooting will wind up being at 100 yds or less. Great practice for learning fundamentals, though, and cheap enough to shoot A LOT. Still no irons, though.
Come to think of it, iron sights are becoming something of a rarity on new boltguns, and are often considered a maybe nice-to-have, but unnecessary, backup.
You could do a Mosin for under a $100 and buy a couple cases of surplus ammo with the rest of your budget. Cool milsurp factor, full power cartridge, but they're not new, if that's what you're looking for.
You would have a lot of fun with any of these options.