Public service announcement: The Genuine Buddy 125 the author apparently bought ("Genuine" is the brand, not a descriptor) is not a moped. At 125cc's, it is legally classified as a motorcycle in most/all jurisdictions and therefore requires a motorcycle license as well as motorcycle insurance. He did at least mention the insurance. The author links the Texas moped/motor scooter law which says bold as brass on the linked page that the moped classification encompasses bikes with displacement no greater than 50cc's, but the implies a license is not required for his particular bike. If he is riding this without an M endorsement, he is breaking the law. Don't be him.
While you're at it, you should also take a rider's course as part of your license acquisition process, at bare minimum the MSF safety course. What it teaches you might prevent you from eating shit into a ditch or the radiator grill of an oncoming car in your first couple of weeks of ridership.
Since (see user name) this is a topic I get to talk about a lot, I should also mention that a hidden cost that many aspiring new motorcycle riders fail to account for when they begin their two wheeled careers is your riding gear. At 125cc's, even this little bike is capable of going more than fast enough to deal you significant, life-altering injury or kill you if you fuck up... Or if some dickwhistle in an oversized SUV runs you over. This risk can be mitigated, not eliminated, by wearing proper riding gear. You should budget around $600-1000 for this, for a full kit of serviceable entry level stuff. That's more cash than most people expect.
"Riding gear" is not just the bare minimum of a helmet from Walmart. You will want a quality ECE rated helmet from a reputable brand not just for safety's sake but also because you will find it infinitely less annoying, but also riding gloves rated for contact with asphalt at speed, abrasion resistant pants and a jacket, and sturdy boots. This is before you get into the specialized stuff you will accumulate for dealing with rain and cold and, heavens forbid, snow. Protective clothing will to a wide extent save you from yourself, because you are most likely to be your own source of injury via wiping out due to inexperience if you have never ridden a motorcycle before, especially in inclement weather.
This is not to say I am discouraging anyone from living the two wheeled life. I own seven (7) motorcycles in total, one of which is indeed a 49cc motor scooter that my state classifies as a moped. I ride them whenever possible. But don't expect this to be a -- ha -- turn key operation if you've lived your entire life with a car.