Could I expect good battery life on a brand new Surface Pro 4 i5 4gb RAM/128gb SSD model? How much on basic use for school?
Using OneNote or Drawboard should net you 5-6 hours battery life. There are things that you can do to improve the battery life such as undervolting the CPU etc. You may experience more battery but generally as a rule of thumb don't expect more than that and bring a charger if you think you will need more use.
Using Microsoft Edge will give you dramatically better battery life than using Chrome or another browser. There are some missing features compared to chrome but it's actually not a bad browser and the better battery life is a plus.
Let me know if you would like some more tips about prolonging battery life. I use a Surface Pro 3 but it should still be helpful to you as well.
Also, did you already pick up your Pro 4 or still debating the purchase?