Companies that host Minecraft Servers -- Is 256M even realistic?

Companies that host Minecraft Servers -- Is 256M even realistic?

My kids wanted their server to be public. And rather than having to
forward ports through two routers and worry about keeping their computers
on 24/7, I decided to buy hosting through a company.
There are a LOT of companies offering cheap MC hosting, virtually all
offering a 256MB low-end option for "up to 4 players." However, within an
hour, the server was crashing due to being out of memory.
Is it realistic to run MC Server 1.6.2 with 256MB? And if not, what is a
reasonable amount of RAM? (I see Notch hasn't published any data here, but
I figured there are some experienced MC server admins on this forum who
could lend their insight.)