From what I read about it, the Arcteryx Atom LT is not a rain jacket. I guess it will be all right in a drizzle, or at best a short shower, but not in real rain.
Mostly I wear regular hiking pants on alpine routes. The main thing is that they dry quickly when they get wet. I've also got breathable rain pants. Neither are big brands, and when they're done, I just buy new ones. My legs don't get cold quickly, but on a very cold day, I sometimes use my rain pants as extra layer. I rarely need to though.
This setup works fine all over Europe in the summer. I've got a pair of long thermal underpants too, but I hardly ever bother to pack them. But for the highest ones, such as Mont Blanc, it's a useful precaution to have them.
That said, hiking pants are less suitable for climbing on sharp rock. One time I've shredded in the Dolomites doing that. But I could have climbed in shorts that day. If you are going to climb a lot of alpine rock routes, buying a pair of pants that can stand a lot of wear and tear would be better.
When it's really cold, I've got a pair of warm dungarees that I bought years ago. They were primarily meant for skiing and I've done that, but they are excellent for mountaineering too. I can sit in the snow for a while with them without getting a wet bottom. I don't know what kind of insulation material is in there, but it's something synthetic, no down. I never needed them while climbing in Europe, but they were fine in the Andes.
As for boots, there are loads of threads discussing that topic. You might want to check them out specifically. The short answer is that what is a good boot you is very personal. If it doesn't fit properly, it's no good, and everybody's feet are different. You just have to experiment.
As for my own boots, I've just about worn down my favorite ones, Millet Rock & Ice GTX. I've used them extensively all over the Alps as well as in a few other places. Got to buy a new pair, if I can find them. They are excellent on glacier routes and on rock, and they are comfortable enough for me to hike a long distance in them. However, they are a bit warm below the snow line.
For colder places, I've got Scarpa Omega boots. They function down to about -20°C, although I do get very cold feet when it's that
cold, especially if I'm not on the move. But they fit really well, they are light and for stiff plastic boots they are easy to walk in. I've also got a big assortment of hiking boots, light and heavy, and some are suitable for crampons.
Depending on the type of terrain and the temperatures I expect, I decide which ones to pack. I go with the lightest pair that I think will be good enough. They've got to be suitable for the terrain, and not so warm that I sweat too much. When crossing glaciers or snow fields, or in wet places like Scotland, water resistance is an important consideration too. Unless it's a short trip, I usually bring two different pairs.My Scarpa Omega boots in their natural habitat