Great question!
There are two things to consider when exploring this question.
#1. Check with your studio and see if they require you to wear grip socks during your sessions. If the answer, is "yes," then you can find the perfect pair based on the style you like. Make sure they have silicone grips on the bottoms to prevent slipping. There are also great style to choose from, like Mary Janes from STRAPILATES, or five toe socks from TOESOX. A quick google shopping search will give you dozens of options.
#2. If the answer is "no," and your studio doesn't require you to wear socks, then you have a couple things to consider. First, you need to keep in mind that the silicone grip socks prevent you from slipping on various surfaces that you might encounter during a pilates session. If you feel sturdy and balanced in your body, you might not need grip socks, but if you find yourself to be a bit challenged when it comes to balance and stability you will definitely want to have grip socks.
Bonus Thoughts: If you tend to have sweaty feet, invest in grip socks. Sweaty feet will cause your feet to slip and slide on the equipment. The same goes for feet that have alot of lotion on them. When it doubt, put on a pair of grip socks!