Congratulations on graduating! My most used brushes are sash brushes, either Purdy’s or Wooster. It’s always handy to have a few detail brushes as well as some chip brushes that you wont be sad about ruining.
In my kit I find it useful to have:
Sharpies, knives (I like snap blades), screwdrivers (flat and phillips) for removing outlet covers and such if you are doing location work, nail set, a hair dryer, nitrile gloves, 5-in-1, a few good putty knives, pencils and charcoal, tape measure, some extra painters tape
The tools you need in your kit will depend on the type of freelance work you do. I’ve never worked a gig where I was expected to bring my own tools to do the job, but it can be helpful, especially on more hectic jobs like in film when you aren’t working in a shop.
Have fun and good luck!