Lots of good advice to follow in this thread!

As someone who's commuted on a motorbike daily, and ridden all bikes extensively throughout the year in Ireland, I feel I have a lot of credibility in this area

Two things I've learned: 1) you cannot avoid getting wet; 2) use ziploc bags / plastic liners for things you absolutely must keep dry (passport, paperwork, laptop, phone, shoes, underwear, socks, etc.)

Generic "dry bags" (as you'd use kayaking / canoeing) can be inexpensive and do work well, but are bulky. Still, ziploc bags should be used inside them, for any electronic gear or paperwork, and "over-doing-it" is no harm.

But expensive bags (Ortlieb, or Kriega, for example) are generally worth it.

If, in advance, you embrace the idea that you'll get wet, you won't be disappointed later; and for precious items, always use a fresh ziploc bag.