You mention that you do not want to sweat so much you are better off with nothing. It is pretty hard to find a rain jacket and rain pants that breath so well that your sweat will evaporate quickly on a rainy day when water is coating much of the jacket and pants. So, if it is warm enough, you might find skipping rain pants might work for you.
I try to avoid hot weather, thus most of my tours are in cooler climates, thus sweat happens but is not excessive for me.
Top to bottom:
A rain cover for helmet is something most cyclists do not use, but I am sold on it. Keeps the top of my head dryer, the water does not run down my forehead into my eyes.
I use some yellow color wrap around glasses in rain when it is not light enough to wear sunglasses.
My favorite rain jacket is a Marmot Precip. I do not use the hood when cycling, but I want a hooded jacket for touring as I often use the hood in the campsite in rain. Sometimes I wear a thin neck gaiter with it but that does not aid waterproofing, it is better to keep my neck and head warm.
Rain pants, the ones I use have not been sold for over a decade, so not mentioning them by model. They are long enough that when I bend my knees pedaling, the bottoms do not lift too high. Zippers on legs that allow me to put them on or take them off without having to remove my shoes. I probably am the only one that does this but I hold them up with suspenders, that way they do not slide down constantly and I do not have to cinch a waistband really tight.
Shoe covers are a must, otherwise the rain gets on your socks and fills your shoes from capillary action. But they only function well if rain pants keeps the water off of your legs above the shoe covers.
If your saddle is leather, a rain cover for it.
I usually store the rain jacket and rain pants where it is quite handy on my bike, I can get it out in less than a minute. Helmet cover and saddle cover in handlebar bag where it is very handy too.
Some long finger gloves are nice too, my favorite gloves are not sold in USA so I am skipping the brand and model. They are not waterproof, they are full finger and give me a small amount of warmth.
If you lack saddle cover or helmet cover, a motel issued shower cover for your head can function in that role too.
I prefer pedals that are two sided, SPD cleat on one side, platform on the other. If my bike shoes are soaked from previous day(s) of rain and it will be dry out, I might want to use my regular shoes that I bring for campsite use on the bike for a day.
Rain, you are not very visible to the drivers behind you that have worn out windshield wipers and ineffective windshield defrosters, so good well aimed taillights are important too.
And you want to be visible too, wear bright color clothing.