Your budget is where I live for most all my scope purchases. Here is what I have bought in your situation. $500-$750.
Leupold VX3i 4.5-14 (good glass for price. low feature, most afordable, set and forget).
I have the 50mm and it is great in low light. Simple dulpex makes it simple design.
SWFA SS 3-15 ffp (reputation for reliability, first choice for dialing at this price). I have not dialed this any, but the reputation gives me confidence. No experience yet on low light performance because it is on an AR-15 right now. Found used for well under budget, well maybe hard to find right now.
Vortex Razor HD LH 3-15 sfp used or LHT depending on pricing. (nice simple MOA reticle, great glass, first choice for Holdover) Nice color and clarity. Need more experience at twilight with this over the Leupold. I got the Razor LH gen 1 used for $600, and there is are 2-10's new still available for under $500.
Trijicon Accupoint. I got a 2.5-10x56 for about $750 a few years ago Black Friday sale. Excellent low light performance, a bit bulky, but not overly heavy. Simple dulplex with illumination. 3-9 power is also well regarded for glass clarity and value.
I have one of each of these, (not LHT) and find each to be great in their price point. My top two recommendations are the Razor LH/T or the SWFA 3-15 depending on how bad you want to Dial. The Razor may have better glass but the SWFA is known for tracking reliability and is FFP.
Others I have not used, but would like to own.
SWFA fixed 10x for $300 also received much praise, or the 10x HD for around $600 with upgraded glass.
Leupold VX5 HD 3-15 or 2-10 also has my eye and will likely be my next hunting scope when I need one.