"Twilight Factor" is a comparative number used to express the effectiveness of an optic for low light use. It is arrived at by multiplying the objective lens dia (in mm) times magnification, then taking the square root of the result. Basically, it attempts to express the idea that larger objectives and higher magnification together helps you see detail better in low light, all else being equal.
The problem with this measure is it totally ignores differences in optical quality. High end optics with lower magnification and smaller objectives will usually outperform cheap optics with high magnification and large objectives. Yet, the TF number for the latter would be higher.
I would totally ignore this number, because it's truly one of the most useless specs in the optics world. Besides the fact it fails to take into account differences in optical design and lens coatings technology, it places way too much emphasis on magnification. It ignores the fact that in order to have good low light performance, an optic needs to produce a reasonably large exit pupil (obj. dia. in mm divided by magnification). For instance, a 10X50 optic would have the same twilight factor as a 20X25. Yet, the former would have a 5mm exit pupil, and the latter would have a tiny 1.25mm exit pupil and substantially less light delivered to your eye. For an optic to have good low light performance, objective diameter needs to be sized according to magnification to still produce an exit pupil of at least 7mm dia or so, in conjunction with quality optics and optimized coatings. Basically, a larger objective allows you to utilize more magnification while still providing all the light your eye can use.
I would keep magnification to no more than 10X personally. If you go much more than that, you don't substantially increase your ability to see detail while handheld because of image shake. Unless there is a corresponding increase in objective diameter, increasing magnification reduces light transmission and magnifies optical aberrations. Moderate magnification also increases field of view and depth of field. For these reasons, I personally prefer 8X42 as an "all-around" handheld binocular.
In your price range, I would look at such binoculars as the Meopta Meostar, Vortex Razor, Leupold Gold Ring, Zen Ray ED2, etc., in 8X42 or 10X42 or 50 configurations.
Right on IMO...
