I agree with the advice already given about getting two pairs - trail shoe and mid.
If you are sure that you want to get the one pair, then you could look at the Salomon Fastpackers. These are mids based on a running shoe (the XA Pro 3D) but are a bit tricky to find in shops to try on. I find them to be a good 'boot' for winter conditions, but again, like others, I'm not sure I would want to run in a mid.
You could also try a shoe (more flexible for jogging) and use with gaiters (eg Keen Targhee and many others). I've used full gaiters and found it works well, as long as you spend the time to get them to fit tightly.
For all footwear with a Goretex/Event/etc lining, it might be a bit of a lottery how long it remains watertight ...certainly over 1000 miles.
But as others have said, whatever the option, fit is everything.