Mesh and offset are two different categorization of dish antennas. Dont get confused and mix them.
Basically satellite antennas can be classified as Solid and Mesh. Solid is plain metal sheets and Mesh as the name indicates look like a metal mesh.
Again the satellite antennas can also be classified as Prime Focus and Offset. The Prime Focus Antenna is a dish which is perfectly round. The focal point is in the middle of the dish. Offset antenna is a dish with oval shape but symmetrical. The focal point is not in the middle of the dish, but to the side of the dish (offset).
All have their own pros and cons.....
Now coming to your query, C band can be received on almost any of the above mentioned type. but to receive Ku band a general preference is a Solid Offset dish.