I want to swap the small pex for 1/2” and am fairly handy and I’m pretty sure I can figure out the pex stuff but am not sure what to do with the current shut offs that are in the basement. Is there an adapter that I purchase that will make the shutoff to pex connection?
Easiest is going to be Push-to-Connect 1/2" Coupling. You will be able to cut the 1/2" copper and then use the SharkBite Push to Connect Coupling to switch to 1/2" PEX the rest of the way up to your vanity. Then you will have to figure out how to connect the 1/2" PEX to the sink and include a shut off under the sink. If you have access to the wall behind the vanity then I like to put 90-Degree Drop-Ear Elbow with a 1/2" Chrome Plated Nipple followed by a 1/2 in. x 3/8 in. Angle Valve.
This Video does a good job of showing it: https://www.youtube.com/watch?v=DL1NL_9Yd1U
I'd leave copper shut offs in place. Assuming you can solder, turn water off, cut copper (leave enough extra room to get a couple inches into vanity...or drain and unsweat valves...cut holes in back of vanity, reinstall new or same valves...pex is cool but if you like secured, solid valves best...that is 1/2" cop x 3/8" compression btw...no need for pex tool...unless your movnng the lines?