I would go for Ubuntu personally. It'll run on 512MB of RAM but it did get a bit sluggish at times using it on old systems with 512MB in my experience. But if it's simple stuff like you said, I'd go with it. Let me know how you get on!
I am running Peppermint Xfce on my laptop for uni.
It is only a little 10" machine with an intel atom n450 (i think) and 2GB ram. While it is certainly not a blazing fast experience it gets the job done.
Manjaro is the beginner-friendly baby brother of Arch so if you choose that you can easily browse the arch-wiki for guides. Xfce is a lightweight desktop environment which doesn't lack in any features.
Arch is also good, but both of these distros require some knowledge, Ubuntu Mini will be better suited than ubuntu for your system, I would recommend Arch over all though, the beginners guide is a good source for first timers.