Cheap upside-down quarry:
1x Transposer (or obsidian pipe)
1x Engine for filler
Tubes/pipes/chests for storage
This quarry will work from the bottom up, so you first have to dig down to bedrock.
Once there dig one ditch that is 13 blocks long with 2 block digged inwards in the middle of the ditch and the transposer fitted there. The idea is that if you put water in the ends of the ditch it will run into the transposer.
The next step is to dig out the quarry bottom. You can use the filler as help for this. You want to have it as wide as the initial ditch, and then any depth really, though you want it all to be covered in running water which will transport any items dropped on the bottom to the first ditch, which will then take it to be sucked up by the transposer.
Finally you set up the filler area to exactly cover the bottom and then any height you want, up to the surface even. Though the best goodies will be aquired in the initial levels. Set the filler to a clear pattern so it clears out everything, and then connect the engine to it and start!
This is a quite quick quarry, and pretty cheap to build, the worst cost is 8 gold for the filler. It also tends to bunch the dropped items together, at least the cobble so you won't have that much items flowing around in your tubes which is good.
Although I would think this particular quarry might not be super appreciated on this server due to the high number of drops it produces (although they are all sucked into our system pretty quickly) and all that running water. It won't keep any chunks loaded which might be appreciated, but that instead means you have to babysit it if it is to work.
I leave it up to the admins to decide if this is acceptable or not, but in any case it's a great way to mine efficiently early on in your single player games