I like to play minecraft which xbox is better for this type of game a 250gb or 4gb?

It doesn't matter.

4 GB will be ok for minecraft but realize that if your want any other games you will have to get a hard drive because the most recent 360 games require you to install 5+ Gigabytes of data but since 360 hard drives are cheap a 4GB will be ok for now…

Considering you probably will use it for other means, for sure get the 250. 4 is basically useless.

You want a 360 with a hard drive.

250 is always better

For Minecraft, either one is fine.

If you plan on other games, or if you get Gold and so get the free Games with Gold then you'll probably want the 250 GB model. It's easier than dealing with USB drives for additional storage.