I used to tour Ireland in the 90's and I found that it's best to wear whatever dries the fastest and covers your body.
To that end I found trekking sandles the best footwear for preventing trench foot. And covering up for the sun (Long sleeves, fingerless gloves, shorts that go below the knee) as the rain and sweating will reduce the effectiveness of your sunblock.
I got the worst sunburn of my life cycling from Belfast to Rosslaire over three days yet it was raining most of the time.
I was brought up wearing shorts all year round so you may feel the cold more than I did. I can only remember one autumnal evening where I especially felt bitterly cold cycling into a chilling northerly wind coming off the Atlantic.