As an instructor when traveling for a workshop, to remove stress or wondering if my supplies will make it there on time, I usually send everything ahead. I don't want to be surprised or have any potential problems with TSA right before I board on a plain. It is much easier if I pack everything in a suitable size suitcase and ship it.
As a student you won't have to carry as much as an instructor but travel can still be stressful. So here are few things you might want to consider, if you have enough time send it by ground this will cost less and take 5-7 business days (depending on the location). If time is of the essence you can choose three day FedEx air service but this will cost quite a bit more.
You can usually carry a portfolio as one of your carry on items, but some smaller planes will have smaller overhead compartments, in most planes there is also small closet but you should always check ahead with your airline.
To prevent damaging the hair on brushes I like to wrap them tightly in a Bamboo brush holder so they don't move and can still breath. For extra protection: if the brushes are damp, I'll place a paper or terry towel next to the hair. If dry consider gently wrapping the tip with plastic wrap. In any case after you have prepared them roll them tightly then with a band secure the top and bottom so they don't move and are safe.
Paint - Carry-On Regulations
Watercolor paints can be packed and carried on, but are subject to TSA's liquid and gel restrictions. Each tube of paint must be less than 3.4 ounces, and all tubes must be packed in one clear, zip-lock plastic bag along with any other liquids and gels you are carrying on board for personal use (all of your liquids are limited to one quart size bag).
Although watercolor tubes are permitted, they may show up in security scans, especially if they are in metal tubes. Bags containing watercolors are relatively likely to require extra inspections. Facilitate this process by packing them in an accessible way, for example, in their own bag or compartment or as the top layer of a suitcase. A clear plastic bag is also convenient in case of security checks.
Checked bags should not be locked, in case the contents need to be inspected. Sealed containers are under extra pressure during air travel, especially in checked bags. Paint tubes usually travel well, but it is possible for them to burst due to this pressure or to rough handling. It is best to pack liquid paints in a double plastic bag inside your luggage.