As a U.K. golfer I spend most of my golf life either playing in rain or waiting for it to come in. Even in a sunny day in July we keep waterproofs in the bag.
So here’s the one thing you need to know - while its nice to be dry and comfortable, the only thing that actually matters is your grip on the club. If your hands are wet and the grip is wet, you’re not hitting anything well. Invest in the best rain gloves you can buy. I have FJ rain designed suede ones that work well. Buy 3/4 of them and keep them in a ziplock like Laz suggested for towels. And you need lots of towels to dry the grips before you play. If it’s really bad keep your hands in bags between shots if you can.
Then get used to prepping a shot under the umbrella. Once your hand and grip are dry spend as little time as possible out in the rain.
As for clothes it depends on how warm it is. In summer I’ll just stick to shorts as bare legs dry quicker than any material and you can move quicker. Your feet will always get wet. Just accept it. Up top it’s all about freedom of movement. Buy something big and loose, not fitted. If it’s still warm enough a gilet is better. Just let your arms get wet. And take a couple of shirts in your bag. If you have a shower, then it dries up it’s nice to be able to change out of the wet shirt.