Minimum RAM needed for Minecraft server?

Tip: If you want to spare more memory, you may set the -Xms parameter even lower, say:

java -Xms32M -Xmx512M -jar minecraft_server.jar nogui

The parameter controls how much memory is reserved on startup. Your server will start with 32MB RAM and whenever it needs more memory it will allocate some until it reaches the maximum of 512M. However, this will result in a little slowdown whenever the allocation is done.

Source: http://www.minecraftwiki.net/wiki/Tutorials/Setting_up_a_server#Less_than_1GB_free_RAM

Also you can check this website : http://www.canihostaminecraftserver.com/

With this you can have a small idea on how many players you can handle :D

If I remember correctly it's about 10 MB per expected user. However, it is also assuming that the players will stay somewhat close together, if everyone spreads out then you'll need a signifigantly higher amount of ram.

256 MB is most likely too little. Minecraft will start alright, but once the world becomes large enough by either exploration or lots of constructions (which your sons probably managed to achieve within said hour), 256 MB is too little and the machine will start swapping, i.e. re/storing parts of RAM to the disk, which both time-consuming and futile since here one single application requires all the RAM. From experience I'd say 512 MB is the absolute minimum for an acceptable performance for two players who don't stray apart too much. But as this other question suggests, even 768 MB purely dedicated to a standalone vanilla Minecraft instance (a server doesn't need all the RAM a standalone Minecraft (=client+server) needs, but probably not much less either; and remember, there's an OS running in addition, and even a tiny Linux distro will still use up some RAM) are too little.

So, no, 256 MB definitely won't do. 1 GB should be ok for small localized projects, but once you want to allow players to spread across the world, even 2 GB may not suffice. Of course, for larger communities, you should consider using e.g. bukkit with a permissions plugin such that only some dedicated areas of the world can be (permanently) modified, allowing the server to save a lot of RAM.

By the way, one interesting alternative to using a host is building a dedicated one of your own, e.g. on a ~50$ Raspberry Pi, which apparently can manage around ten persons at an acceptable performance. edit And maybe http://pi.minecraft.net/ will improve this even further...