Sounds quite ambitious. My thought is, if you are going to do all the work of building a frame, better have the purpose for it. Does a family member need a house addition? If they pay the materials, you build the frame for them. Better that relatives get your free labor(or lower cost labor) than strangers, eh?
I wouldn't want to build a frame that is not intended for a specific purpose.
The frame should be your design. At least it should be your overall dimensions, and if need be, specifically designed by someone else. With a plan in hand, it's down hill from there. What you could do, is order oak brace stock, let it dry, and then cut braces for the frame. If the brace stock is sufficiently dry, it will be stable. You can then see how you like working the dry wood compared to green wood. If it suits you, you can order the other material and let it season some before cutting, increasing the stability of the pieces.
I agree that to dry the wood, you want to properly stack it, seal the endgrain as quickly as possible to prevent quick drying from the ends, and encourage slower more even drying from the sides, and keep the stock out of the sun. The sun will dry timbers more quickly and likely unevenly.
Some may say that cutting the wood dry is more difficult than wet. How much more difficult is my question. I've cut some dry white oak that didn't seem bad to me, though not a whole frame. Sharp tools are important.
By doing a dedicated design(without a firm timeline) and starting with braces etc, you get to test the waters without having to buy all the wood or build the whole frame at once.
Best of luck and let us know how your class went.