It looks like that model shipped with 1GB of RAM and 1 empty slot but is upgradable to 4GB. [1] My advice would be to upgrade the RAM if it practical [2]. This would make just about all distros practical. It's probably worth considering a cheap SSD as well...it can always be installed in another system later.
Of course, those are suggestions that involve spending a little money and the reason is that I would generally recommend standard Ubuntu. Not because it is better but because it has its own StackExhange site for getting help: https://askubuntu.com/. For me AskUbuntu is the killer app that trumps pretty much every other consideration. That's not to say that I don't use ArchWiki and other resources (like man pages) but the Q&A format focused on Ubuntu can provide more focused advice and solutions. Ubuntu also feels more beginner friendly than some other distributions of similar size, the defaults (arguments about Unity and sysmd aside) are relatively sane and there is a large selection of binary packages so the joys and sorrows of compiling from source can be approached with on gently graded slope. Worry not, there's enough sources of WTF and frustration for someone new to Linux without working with source.
Good luck.
[1]: https://www.cnet.com/products/fujitsu-lifebook-e8410-15-4-co...
[2]: US ebay shows a 2GB stick of PC-2 5300 can be purchased for ~$4.00 including shipping and 3GB is enough to make "mainstream" Linux distros an option.