For an adult or kid?
I think your chambering is a very good choice.
There are myriads of bolt action .223s (and pumps and levers too).
But since you want irons, it might be hard to beat a CZ 527 - the carbine with the short barrel and irons.
http://www.gunbroker.com/Auction/ViewItem.aspx?Item=439106178
Or the FS is what I'd get in that situation:
http://www.gunbroker.com/Auction/ViewItem.aspx?Item=430160312
Edit: Oops, wait - sorry, those are over budget. Ignore above. In that case...
Hmmm, are you willing to go used, or new only? I'd definitely go used on that budget, and look for a good deal on an old Remington model
seven with iron sights in .223 or .243.
Find something old - like 1970s or earlier, when most rifles had iron sights. Your usual suspects -if not a Rem Seven, then a Ruger 77, Rem 700, Rem 788, Win 70, Browning A-bolt, etc. It'll be just on the edge of your budget, and you'll have to be patient, but that's the best call on that budget. New, you can't get there from here - new Savages and such don't have irons (do they?).
http://www.armslist.com/classifieds...sellertype=1&tag=bolt-action&tag=223-556-nato
Now, the Mossberg MVP (one of the variants) does meet the criteria, as someone said, BUT it has a detachable mag (can be good or bad depending on your viewpoint - I say bad), and the sights are pretty cheap. And well, it's a Mossberg. I just cannot shake being leery of that bolt action since the bolt-through-the-face stories from a few years back. Just a cheaply-made rifle.
Think OLD, meaning quality and value for your dollar. There are many used guns out there which have been barely shot.
http://www.gunbroker.com/Bolt-Action-Rifles/BI.aspx?ca=5000020
[Oh, and nothing wrong with asking variants of the same question over and over - no harm, no foul. If you're saving up, why not gather as much info as possible, espec. if that process is itself fun?]