OK... this is under the kitchen sink right? Then it's a 5/8" copper supply line with a 3/8" adapter to the faucet.
1st. There should be a stop valve on the 5/8" supply line. One each for hot and cold. These aren't there now.
2nd. Purchase your faucet before you get the "stops" (shut-off valves) and see what kind that you need. You might need "risers" (the stainless flex hoses) and need to know how the supply to the faucet is configured. I only say this because here in Calif most of the stops have a 1/2" outlet. I just installed a Moen faucet (my preference) and it came with attached hoses with 3/8" fittings. If you have any questions take the faucet with you and ask someone in the plumbing dept. I can't guarantee you'll get the right answer, if you go to the big boxs, but it's worth a shot!
If you can't use the nut and compression ring on the lower pipe you will have to either remove it, use a Crescent (adjustable) wrench, adjust it to just slightly larger than the bottom pipe, hold it against the bottom of the nut and tap it off (upwards) with gentle hammer taps. If that doesn't work you'll have to cut the pipe. Make sure it's very clean (remove paint) and install the new stop.