Reload.
It's notably cheaper than paying retail prices for factory ammo.
Or, if you look at it the way that many of us reloaders do.... You get to shoot 2, 3, 5, or 10+ times as much as you can when paying for factory ammo.
If you're not interested in entertaining the though of reloading....
Remove the gas tube, flip your gas block upside down, and run the AR as a manual repeater.
I have an upper operating in that fashion. Though, there's more to it than just wanting it to be a manual repeater. (Testing and explanation to come in the future. I paid $11 for the barrel and $8 for the gas block.
)
For something "off the shelf" I'd be looking at a Ruger American or constantly checking Gunbroker for guys that are off-loading discontinued Marlin X7s. Though the .223 version is never as cheap as the standard short action or long action 'calibers', it can still be found for less than $250 if you're patient (and willing to take on an "orphan" rifle that has no factory support).
I wouldn't touch a Handi-Rifle unless I could shoot it first. They're even worse-off than the Marlin X7s, in their obsolescence and lack of warranty support. (They were also discontinued, if you haven't heard.)
For $150-200, your best bet is reloading...