I have a three season bag from Mountain Hardware, cost about 80 quid, it was a million times better than the 40 quid bag it replaced so IMO worth every penny. You’d need a bivvy bag too if you have no tent.
Cold is better than wet any day. Just put more clothes on. TBH if its less than 5 degrees, it doesn’t make much difference how much less, as long as you’re out of the wind.
My kit was:
Alpkit SH800 bag
Alpkit Hunka bivvy bag
Alpkit Airo mat
Alpkit titanium folding spork (had to have one of those!)
Little gas stove from Go Outdoors and a bag of their all-day breakfast.
Spare set of cycling kit to change into for sleeping / day 2 (although I didn’t use most of it as funnily enough I didnt actually get sweaty)
All fits in a medium size rucksack with the sleeping bag on a cheap plastic rack which clamps on the seat tube (which I pinched off my daughters bike).