I have a compact 50/34 crankset, Miche (Campag) 12-25 cassette, Campag Xenon 10 speed short cage rear derailleur and Kmc DX10SC chain on my Bianchi road bike. I would like to change the cassette to a Veloce (or similar) 13-29 and understand that I will also have to get a medium cage rear derailleur. Would any of the Campag Veloce/Mirage/Xenon medium cage derailleurs do the trick? Also it has been suggested that I may need a new chain. Does anyone know exactly what I need (apart from stronger legs)?
Yes, any 9 or 10 speed Campy rear derailleur should work on your setup. You may be able to get away with keeping your existing RD and chain, but you won't know until you try it. You may lose the ability to shift into the big-big or small-small front-rear gear combinations.
So aside from the cassette itself, worst case you might need to replace your chain (Check Ebay, DX10SC's are all over the place for around $30), and your RD. Expect to pay around $40-$70 for a lower-end Campy RD depending on group, from a place like Ribble Cycles.
One other detail: since your existing cassette has a 12T small cog, I think you can reuse your current lockring. Campy seems to have started including lockrings with new cassettes lately so this should not be an issue anyway. They used to make you buy them separately for some hefty fee (like $25), and they have different sizes for cassettes with 11T small cogs vs 12T and larger, so you had to worry about whether you had the right size. I believe 12T and 13T cassettes use the same size though, so you're covered whether the new cassette includes one or not.
If you have 10-speed shifters, cassette, and chain any 10-speed Campagnolo medium cage rear derailleur will work. A pre-2001 9-speed derailleur will not work because the actuation ratio was changed that year. I'm not sure when the medium cage RD's were introduced. Some riders have reported using a short cage RD with the 13-29 cassette but I cannot confirm that it will work.
Whether or not you need a new chain depends on how much the old one has worn or stretched. You need to measure the chain. A 24 pin interval of new chain will measure exactly 12 inches. By the time any 24 pin interval measures 12 1/16 inches it needs to be replaced. Roller wear should also be checked with a chain checker tool.
Buy the new chain. If you are in the large CR in front and go the large cog in back and the chain isn't long enough you can really screw things up...a lot more expensive that a chain. The cross shifting with a compact setup is a lot more frequent and a higher probability of an "accidental" shift big big.