Hosting files takes almost no CPU power. If you're running in to trouble on anything you're transcoding, which means converting the files from the format they're in on disk to something else for streaming (usually to reduce the bitrate for internet transmission or because the player doesn't support the native format).
If you aren't streaming over the internet, disable transcoding and you're more or less only limited by bandwidth.
Really? Idle, my Jellyfin instance has about 260MB resident right now. I don't think I've had any memory issues while in use; the old Mac Mini (running Linux) I have it running on only has 4GB total, and it's also running a couple Mono-based apps that are a bit more memory-hungry.
Jellyfin runs on about 700-800MiB of RAM for me. It sounds like you're hitting a memory bug if you're running out of RAM just serving files, to be honest. I've never used Plex but I doubt it runs with just 70MiB.
Perhaps it'll use much more RAM transcoding, but I'd still expect a dedicated 2GiB to be plenty for Jellyfin even in extreme cases. I doubt you'll get any decent transcoding speed out of ffmpeg if you need a buffer that size anyway.
Plex, its costs-money competition, transcodes files for playback (using `ffmpeg` or `libav` iirc). Is `jellyfin` less capable in this department then or something else?
I'm running Jellyfin on a recent Intel-based Synology (they also have cheaper ARM CPU models), and it can transcode H.265->H.264 on the fly using about 50% CPU. It also runs in a Docker container so it's pretty easy to manage. I'm a big fan!