How much RAM does a Minecraft server need for a Spleef arena?

The amount of RAM will depend on many factors like: the amount of players, the size of the arena,whether there is flowing lava or water, etc so it is very hard to gauge how much RAM is needed. I would generally use about 2GB of RAM for my servers.

A vanilla server with a 30 people max would use about 2 gigs of RAM. But depending on what plugins you use for the server, you could use a lot more than that. If the the plugins for spleef isn't that big, and you only have a few other plugins, I'd say about 2.25 RAM should be plenty to keep your server running smoothly.

I use a 16 slot server with 512mb RAM but mine's a hoster; I have like 10 plugins and it doesn't lag.

Hosters rock, I recommend them. My friends got a 1.5 gig one with 42 slots from beastnode and it runs fine even with the 42 people on, normally only 18 though.