1995 Honda Civic Strange Sound at Cold Start

I'm just beginning to learn about auto mechanics, so bear that in mind.

I had some trouble with my car about two weeks ago. It was stalling, and that got bad really fast, so I took it to a mechanic near my work. He said he replaced the ignition rotor and the distributor cables. After that, the car seemed to run fine, but I noticed a different problem.

When I start it in the morning, it sounds very odd. If I had to take a wild guess at what I'm hearing, it's the sound of the engine turning without combustion, or with less-than-usual combustion. This lasts about 10 seconds, then it sounds like normal, without me doing anything more. It's just strangely quiet for a few seconds.

I don't plan to repair it myself. I took it to the same mechanic today, and he said he didn't see anything wrong, and maybe I should leave it overnight so he can try it cold.

I'm hoping someone can give me a diagnosis: something like, the problem is likely X and it will cost you about Y to have a mechanic repair it.

Thanks for your help.