For hiking I wear a thin liner sock (knee high compression), and a mid-weight wool sock, year round, any location. Keeps my feet warm, not sweaty, and prevents blisters.
I would highly recommend against a poncho for rain, as the wind can be wicked and the poncho will not provide any sort of good coverage. Honestly, cost is not important, but more expensive can mean more features so it's really what your priorities are. My rain pants were fairly cheap, $40 I think? I love them, particularly as they zip all the way up the sides so I can put them on over my boots. They are also light weight, and I can roll them up and fit them in a quart size ziplock bag in my backpack. My jacket (gortex rain shell) was $250, but worth every penny. The cuffs tightened around my wrists, the hood had 2 different ways to adjust it to keep it tight against my head, the sides had zippers for venting, and all the zippers were seamed to keep rain out. We spent a LOT of time in the elements (we did a 40 mile, 5 day, hut to hut hike along with several separate long day hikes) in the rain and I stayed warm and dry. If you don't need that level of protection, cheaper would be fine.
It is possible to do Iceland carry on only, but you'll likely need to keep your bulky items on you, and if flying IcelandAir, you'll need to abide by their stricter rules.