What material were your 1.6mm panels, stainless or galvanized mild? I've only used 30mm punches in 1.2mm mild steel and they were a work out on their own, I bet the Bishi Bashi buttons really got you sweating! A decent allen key and a long bit of pipe is a must for those!
I'm hoping the carbide tipped hole saws should yield good results, they have from the reports and videos I've seen from them. Standard hole saws don't work very well as they don't cut as well and there is less room for swarf evacuation resulting in double cutting and increased rubbing/decreased tool life. I would be surprised If I got more than one hole from a standard HSS/bimetal etc hole saw.
I definitely wouldn't recommend a cone/step drill though, I tried one of those once and they're shite
The carbide tips are a lot tougher, stronger and have a have a lot more room for swarf evacuation. The brazed inserts will have a sharper edge and better cutting geometry which should stay sharper for longer and should cut rather than rub. Freely cutting the material should give a nice hole, rubbing is where you'll get a crap finish.
Cutting conditions and feeds/speeds will also have a big impact. I can only eyeball the feed rate but I can calculate the optimum speed rate (surface meters/min). The material wants to be clamped well and supported well from the back too. You want to use a similar piece of sacrificial material to minimize the burr on the exit of the hole. If you just use a piece of wood for example then the burr will just pull into the wood. If you use some scrap metal then the burr doesn't get chance to form as the rear of the hole is fully supported and the cutter starts cutting the sacrificial material before the burr gets chance to form. Cooling/lubrication of the bit is important too.
The smaller buttons only need a 25mm bit which are easy and cheap enough to pick up. I need a 57-58mm bit for the larger buttons though which are not as common and certainly more expensive! I found some cheap Chinese ones but I don't really like buying cheap tools. I've found some suitable German ones but they're about 4x the price...