Any chassis is going to be significantly over your budget before you get a stock and grip. If using AICS mags is your thing, maybe try a Boyds stock like the Pro Varmint ($129) and have CDI Precision inlet and install their AICS-compatible bottom metal ($209 for parts and labor)? I've excluded shipping costs, naturally, and things like pillaring and bedding the rifle would be extra as well, but that would get you on a decent path that you can add to later as your skills demand it and your funds allow it.
Something a bit closer to a chassis in terms of metal-to-metal contact would be a Choate Tactical stock. I'm not familiar with that particular stock, but I think it requires you to obtain Savage factory bottom metal (and a Savage factory detachable magazine) for your 12FV or have an outfit like CDI inlet it for their AICS bottom metal.
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