I don’t used Steam for this reason, Eve Online has a launcher sucking up my RAM already at an alarming rate, Steam is just a simple method to install a Wine overlay, they called their version Proton. If you are running 16 GB RAM, or better then you should have no issue running Steam, Proton, Eve Launcher, and the Eve Client. If you plan to buy 2 or more omega accounts to multi-box ( which is allowed ) then you are looking at using a lot more RAM.
I can run this game on a 12 year old box, with 8 GB of RAM and a 2 GB passive graphics adapter. I do have to kill the launcher once the client starts. also avoid Jita like the plague as the 900+ players there cause networking issues, lag, and disconnects.
I had no issues using both Xubuntu or Manjaro, when testing Manjaro had better performance and was very simple to set up. Back in June of last year, I set up Eve to run in Manjaro. I never tested Linux Mint, but it is the preferred version for Windows users making the switch. My crossover OS was Kubuntu back in 2010, but all the doodads and fancy toys made it bloated just like Windows OS.
Lubuntu and Xubuntu are both slimmer versions of Ubuntu OS and Mint is another flavor of Ubuntu. Manjaro is Arch Linux, mine is using the XFCE Whiskers menus and I set mine up to mimick Windows XP desktop.
Steam or not to Steam is the real question. You can move your Steam Eve account to Eve by using the Steam icon to log into the main webpage. Access your account and change password. CCP’s webpage will notice you are running it through Steam and offer to set you up with a new User ID and password to access your steam account without running Steam. Launch Eve using Wine and you have one less program running in the background.
Fly safe o7