Do you sit until the last minute of legal time or do you go home when you can't see with the naked eye? If the latter, a red dot with lighter lens coatings and NV levels will get it.
Otherwise, I have not seen any LPVO that was bright enough in the woods. The objectives just aren't big enough. The classic answer was a 1.5-6x40, but times are changing. Your budget may mean you need to shop scopes that do what the 1.5-6x does within a greater magnification range.
50' @ 100 yards field of view is enough for close shots. That usually equates to 2x. You can work around this if you practice with a brightly lit reticle, shooting both eyes open. You'll hit a little off horizontally. I find I lose the knack if I don't practice it.
6x on the high end with a 40mm+ objective is enough for the edges of legal shooting time. The worse your eyes, the more you spend and the more likely you are to need an illuminated reticle. If you're over the hill, plan on your eyes getting worse and spend more to save in the long run. Europtic has S&B and Zeiss 1.5-6x that would relieve you of having to wonder if got something good enough.
