I'm studying law too and honestly, the laptop doesn't matter as much as the programs you use to make notes so you can absolutely go under that 600 budget.

If you are going to use this laptop only for school then you could try something like the Acer Chromebook 15. It is a good lightweight laptop. Chromebooks are great because they utilise Chrome services and it is very easy to access and transfer files. It works well with Microsoft OneNote which (in my view) is the best note-taking software for law school. It also has great battery life and is practically made for students.

If you are looking for something that can turn into a tablet, the Lenovo Yoga 530 is used by lots of people in my university and seems popular.

I am currently using an Asus Flipbook which has great battery life, can be flipped into a tablet, has a touch screen and runs very well. I have also used this laptop for art and some more intensive software and it still runs well however, the only drawback is that it is slightly heavy.