Since you're asking this I'm guessing you don't have a lot of experience biking in the rain. Which brings me to my advice part. Try biking for a while in the rain here in the US before you devote a considerable amount of your vacation to this.
There really is no perfect solution to staying dry and comfortable. When you bike, even at a modest pace, you build up heat. Sweat ("glow" for you ladies) is your body's way of cooling. So for a brisk hike or bike ride there are really 2 incompatible goals - water you generate out, no outside water in. An ideal clothing system would offer no resistance to sweat leaving your body (or, even better, wick it out) but complete blocking of external water coming in. There are new "miracle" fabrics for jackets announced each year, but the truth is none of them really work that well. That's why any of the technical wear for biking/hiking/climbing are loaded with pit zips, arm zips, front pocket mesh liners, zippers that have pulls on both ends to open a gap, etc. because they know they just can't get all the moisture out of the jacket thru the fabric.
Water vapor depends on a difference in humidity to move, but if you are generating water vapor thru work on a rainy day when the exterior humidity is 100% then the vapor off your body doesn't tend to work thru your clothes. So people wear all kinds of clingy synthetic wear in an attempt to wick moisture from their body to somewhere it can escape, otherwise you feel clammy. Still it all ends up as a compromise. You are not going to be warm and dry biking around, unless perhaps you are riding very slow in an area that is very flat. And keep in mind that a jacket is just part of the outfit you'll need. Even with fenders, water will get everywhere. You'll need waterproof pants and booties, along with some gloves. Gloves get water inside them, even if Goretex and completely sealed, and once wet inside are not easy to slip back on.
Even with a hood and brim on the jacket, water will still hit your face. Sit outside for a few hours in the rain and some finds its way down your neck in front. Also the water hitting your eyes makes it hard to see, so you'll need to wear some clear or yellow-tinted glasses, which themselves will get a bit blurry and be another source of water dripping onto your neck. And cold throws in another twist. Starting out you may be cold, but its not convenient to remove layers in a downpour as you warm up while riding. Honestly, biking in the rain isn't a lot of fun. People do it, but you don't see them smiling ;-)