It is a lot about individual preference and local climate. Also about what type of riding you are doing, how far & how fast, commuting vs training.
I'm a commuter and it is a short relatively flat commute so I don't have to worry as much about sweating. If possible I try to get by in normal clothes, at most I bring a clean shirt to change into. So I don't have to have a lot of specialized bike clothes.
If I did a lot of longer rides in inclement weather I'd look into things like arm warmers, maybe.
For cold weather I do have some specialized stuff. A merino wool undershirt. A windbreaker. (I like it mainly because it is thin, it is shaped right, and it provides me an extra layer but I can still get the outer layer on over it.) And a rain jacket. I splurged on the rain jacket & rain pants. I use them more for cold weather than for actual rain. They are Goretex (from Terry), and they block the wind & cold while allowing the body heat out--I still get sweaty in them, but not as sweaty as fast as in a cheap plastic raincoat.
My rain pants go over my slacks or jeans, whatever I'm wearing that day. If it's too warm for the rain pants, I prefer to bring a change of clothes in a plastic bag, rather than go to the effort of trying to stay dry. When it's cold it's worth it to stay dry, cold rain is so uncomfortable.
There are a lot of other threads about weather & gear you might look at, use the "search" feature.
As far as changing a tube, that's an important skill but a more important skill is cleaning your chain. Search for relevant threads here, and/or look for youtube videos. But what I'd really recommend is go to your bike shop and see if someone will show you how to do those things. Some bike shops offer classes.
2009 Trek 7.2FX WSD, brooks Champion Flyer S, commuter bike