Most modern computers don't have those ports now. My workstation computer (true workstation, not just a tower that one does work and only work on) does have those ports and it's just 2 yrs old, but most computers bought off the shelf anymore don't.
The USB to Serial is probably your best/cheapest bet, but I would make sure that it has drivers/software (for your cutter) for Win 10 64bit as that is going to be the system that it's going to be on, not Win 7. While there used to be some compatibility between OSs, Win 10 (at least my experience with my dad's computers (I stopped using Windows on bare metal when Win 10 came out)) is very much a fickle OS, I would make sure that everything is kosher for that specific OS.
Depending on the USB to serial cable, may have to make sure those drivers are for Win 10 as well and not all of these cables are created equal. I know I couldn't get the cheapest to run my embroidery machines connected directly to the computer (not the same one as my workstation).
The joys of upgrading some hardware, may force one to upgrade other software/hardware as well. That could be possible.