Help with cold start engine problem

Hey guys, I've just recently bought an Ap1 Honda S2000 and I must've only test driven it while the engine was hot. Once bought, the next day I started up the car and I noticed the engine was stuttering or consistently changing rpm while warming up. It almost sounds like the car will stall, but it hasn't yet. When the car is warmed up, idling at traffic lights/stops everything is OK.

Is this a common problem? And is there anyone out here that can advise what to do? If not directly advise a mechanic what to look for?

Please view below video of current problem.
https://youtu.be/9awk0cpF4C0

If it helps, I'm also located in Sydney.

Thanks all.

When starting the car, try pushing the button in harder

On a serious note, could be coil pack issue

Really? I'll try that next time, but I usually press the button just to get the car started.. any longer I feel like I'm going to cause a problem.
How and where would I be able to obtain if that is the problem?

It's not the button, I was joking.

Coil packs can get from Honda

definitely sounds like a coil pack/spark plug issue