Looking to selfhost a family Minecraft server for my kids and nephews. Got it running on an old media server box but it keeps crashing due to not enough RAM, even with just one test player. I was hoping to unveil it as a Christmas surprise until I hit this wall. Anyone have a ballpark for what processing and RAM a small server like this will need?

If you’re just throwing a few of your fav mods together, 4gb can absolutely do it. If you’re interested in a larger mod pack, you’ll want to check the page for the modpack.
Extreme example: right now I’m hosting an “all the mods 10” server for some friends and they suggest at least 8gb of ram.
On the other hand I’ve run a simple pack with a few things like Mekanism and Botania on 4gb no problem.