Solid choice in rifle and chambering.

I'll echo NM448's comment above regarding BDC reticles (my experience has been EXACTLY the same) and budget. I've also been in the boat where my system budget has been consumed by the rifle with little left for the scope and mounts. So, I bought fully intending to upgrade at the first opportunity - which was forced upon me the first season I used that setup when it fogged so badly I ended up having to borrow a rifle. Fortunately, the only mounts available to me were from (the old) Redfield, which that rifle still wears. Know the risks up front.

I'm assuming you're also looking at having to spring for the base and rings with the $200 you have left? That's going to make things tight. Nothing will make a good rifle shoot like fecal matter faster than a marginal scope in a junk ring/base setup. Ugh. I don't envy you here.

Just a quick look on "that internet auction site" and it looks like you can probably pick up a 3-9x or 4-12x Vortex Diamondback for something between $150 and $200. The others mentioned above could be similar. If you're going to skimp on the scope to start with, at least get one with a reputable warranty. I'd highly recommend you put some budget into good scope mounts that'll be worthy of whatever you top that rifle with down the road. Who knows, you may luck out on your scope skimp and not have to change anything?