Metal straws are typically made from stainless steel. In order to make clean/clear marks on stainless, you're probably looking at a 1064nm fiber laser. A 10,600nm CO2 laser (like you find it you search for "laser engraver" on eBay) will technically mark on stainless, but you will struggle with clarity, and you'll be putting a LOT of heat into your part, so you may have issues with warping on thin metals like straws. (For reference, these CO2 lasers are great at cutting/engraving plastics, woods, and papers, but not metals.)

I have used this fiber laser to engrave metals and plastics in an industrial setting for more than a year. It's Chinese, the interface is crap, and the rotary fixture is difficult to use, but this is the absolute bare minimum from what I've seen to get you in the door. A fiber laser like this also allows you the control to change colors, whereas a CO2 is just going to be "burn black" and not much else.

As others have said, you're probably better off contacting some local shops that already own the equipment and outsourcing the work to start, otherwise you're buying a $6500 toy with no guaranteed way to pay it off.