Replacing Bathroom Sink

I am about to replace my bathroom sink. It's chipped and cracked. Basically, looking it's age...almost 40!
The replacement sink is a 19" round Crane fixture, self rim, vitreous china. The old sink needs to be removed from the counter top which has a SS rim frame around the top. Think I can handle that part OK. My question is the new sink does not have a chrome ring around the drain hole which I guess is part of the old stopper assembly. Do I need to replace the old assembly (stopper/chrome ring) or will those parts install in the new sink? I plan on setting the new sink in place using the adhesive caulk around the counter and sink rim, then install the faucet assembly and plumbing connections. Does this seem like a good approach?
Ken

If you buy a new sink it will come with a new drain assembly. If you are using the old faucet, you should prpbably still buy a new drain assemply (tailpiece, p-trap). Just my humble opinion.

That should have read "new faucet" not sink. Hit send to quick

RE; Replacing Bathroom Sink

I did buy a new sink, but there was nothing in the box except the sink and a small tube of "adhesive caulk". Got it at Lowe's. It was a Crane sink and only cost $35. I had the Salesman open the box as I wanted to make sure the sink was in good shape. He didn't mention that anything was missing?
Ken