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?
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?
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