I would prefer to have one dish for C and Ku.
If you want one dish that does both, a good solid would be your best bet, followed by a perf, with mesh in last place. Surface imperfections and irregularities seem to be a fine poison for Ku reception on a BUD but they don't affect C anywhere near as much. Shallow dishes (f/D around 0.4 or larger) are more likely to work better on Ku with combo or ortho feeds.
In terms of size, I get most of C-band on my 7.5' and a good fraction on my 6', but it depends on what you are after. If you drop down to an 8', you'll be losing about 3.5 dB of CNR from your 12', meaning easy can become hard. My 10' performs noticeably better than the 7.5' and they have identical feeds and high-end LNBs.
You could hunt around for a good solid 8-10' to rescue, but that may be hard to come by. The 2.4m Geosatpro, available from SatelliteAV, meets most of the above criteria. You may spend a lot more trying to get everything you want in a single dish and end up with less signal, but if the main criteria is for one dish, that's what you have to accept.