If they are to be used in the woods, and solely in the woods, then I agree - 8x would be best.
This is because ranges are short and field of view will need to be wide due to tracking and trying to locate the subject. And because they are to be used in the woods then light may be an issue so I would go for at least a 42mm lens. A decent set of 50mm roof prism bins would weigh no more than a 42mm porro prism, and would be even better. But they will cost much much more
My only concern is if the OP will want to use them outside the woods, in more open terrain. In that case I'm not sure 8x will give the detail and viewing experience desired at longer ranges (the RSPB may recommend 8x for birdwatching but that's only because many birdwatchers use the bins for locating/quick ID - many will have the ID skills that a close view will not be required - and then use a higher mag spotting scope for the actual observation. Don't be swayed by what they recommend for a specific use if you intend on using your bins for more general use). If the OP wants a more general use of the binoculars and will possibly be using them at longer ranges (and let's be honest, that's likely) then I would go for a 10x magnification. I think I would still stick at a minimum of a 42mm objective lens, especially if going for 10x - it's not just about the magnification but also about the exit pupil and focal length (example - I have a pair of Hawke 10x25s. Last Christmas I bought my mother a pair of Hawke 8x25s so she can watch the birds and squirrels in her garden. I thought my 10x bins gave a great image. But the 8xs ARE sharper, even if my 10xs show a bigger image, although my 10xs give a better view at range). So the higher the magnification, the higher the exit pupil really needs to be, even more so in shaded areas like woods. A 25mm lens really isn't up to the job unless you are spending lots (100s, if not 1000s) of money.
The very best advice for the OP is to try some out.
I would start with looking at 8x42 and 10x42 and deviate from there.