I have an old plastic shutoff valve (see photo attached) that has a 1/2 inch fitting.
http://i54.tinypic.com/t5hszq.jpg
I checked and it's copper piping.

I have a new faucet that needs to fit to a 3/8 inch fitting, so I figure the best thing is to replace this plastic shutoff valve with a new stainless one. Before I attack this, how easy is it going to be to remove that plastic valve from the copper pipe? Will I need to cut it off the pipe? Once it's removed and I make sure the pipe is clean, can I just buy a new stainless compression valve with 3/8 inch fitting like this and I'm all set? http://www.homedepot.com/h_d1/N-5yc1vZ1xh8/R-100050807/h_d2/ProductDisplay?langId=-1&storeId=10051&catalogId=10053

Hi mixart,
Yes, that's the correct replacement. Shut the water off at the house shut off and unscrew and remove the old valve. Try to remove the ferrule and nut. If the ferrule won't come loos try and reuse the old ferrule and compression nut. If that won't work make yout cut as close to the ferrule as possible, Good luck, Tom