Zooming down is an asset, but reliable tracking is an absolute must. I just don't trust anything in the sub-$500 made in China to do it reliably. I'm sure some of them do, but I've seen too many that don't.
I just bought an Athlon Midas myself. It's got good glass, nice turrets, and a really nice reticle. Doesn't track well at all. I fully expected that because it retails for about $400 and is made in China. If you expect anything different, then you're setting yourself up for failure.
At a bare minimum, you could get an SWFA 3-15 SFP. They go for about $450 used and have a really nice reticle. Shooting at distance, you're going to be at 15x anyway so the subtensions will be correct. You'll just have to know for shorter shots when you lower the mag, your subtensions are going to be wrong.
Once you get up into the $600 range, you can look at the SWFA 3-15 FFP, Nikon FX1000, and you're not far from a used Burris XTYII 3-15 or PST Gen 2 3-15 or a used Athlon Ares (I think, not 100% sure on pricing here). But if you're really set on $400 and you want zoom, I'd strongly consider the SWFA 3-15 SFP. Or, get an FFP Athlon and just plan to use the reticle for holdovers for everything.