Both are fine, but the first one is more simple and natural.

Both are correct

Hi, Sophia Linn! It would be correct to say the following: 1. I want to study abroad. 2. I want to go study overseas. If you have further questions or are interested in having conversational lessons with an English teacher, please feel free to message me. I would be happy to hear from you! https://teach.italki.com/teacher/5129645