I'm going against the grain and say that pretty much any modern camera can fill your needs, small or big. You say you don't mind packing larger gear, but for travel specifically, you will feel every extra weight.
First, going with modern mirorrless cameras instead of DSLRs will save a huge chunk of volume and weight out of the gate. Though you would be paying a bit extra for modern stuff.
Second, if you're mostly going to shoot in daylight, going with smaller sensor sizes (APS-C or M43 instead of Full Frame) also cuts down weight for the camera body and lenses. If you're really worried about low light photos, then go Full Frame (but I'd say APS-C sensors are still mostly fine).
There is no right way of learning all the ins and outs of photography settings (ISO, shutter speed, F-stop). Digital cameras already make taking photos so much easier, you can learn all those stuff at your own pace. I'd say stop worrying and just go out and shoot. Get a camera that at least has a PASM dial. If you're not sure about what settings for what scenario, put it to Auto/P-mode. Then, you can try out A-mode and S-mode when you need it. Look up stuff when you don't understand a thing, or want to replicate a certain feel. Take more photos, and learn composition along the way. Sometimes composition is more important to a good photo than the right settings.
Hope this helps!