For low light, you want the best glass you can get. A 50mm objective allows you to use slightly higher magnification, but I do not think that matters a whole lot. With a 42mm objective you get the maximum useable exit pupil at 6x, while with 50mm at 7x.
SImilarly, with fixed magnification scopes you get fewer lenses and more light coming through which can also be very helpful.
Lastly, with typical reticles, you will probably see the target longer than you can see the reticle. That is why a thick highly visible reticle such as #1 or #4 can be very useful.
I am not sure if you can get a perfect low light scope for under $300.
For right around $300 (I think) you can get a Meopta Artemis 2000 6x42 scope with german #4 reticle with some ranging hashmarks. I think that is a perfect scope for your application.
For an extra hundred bucks you can get a IOR Hunting 6x42 with #4a reticle which has better glass than the Artemis (that is the scope I have on my 280Rem).
If you decide that Meopta and IOR are too much money, I would suggest you take a look at Sightron S2 6x42 and Nikon Monarch 6x42.
All of the scopes above have glass substantially superior to Fullfield II or Elite 3200. If you want to go with a variable under $300, it may be worth your while to look at Elite 4200 3-9x40. Probably the best glass in this price range.