If you don't already have one, get one of those four part (pot, deep strainer, shallow strainer, pot, lid). They're excellent for spaghetti; "New England Boiled Dinners;" corn; tamales; "Low Country Boils;" and all that stuff. Get one of these sets first, even if you have to buy an 8 qt. model (but look for a 12 qt. I know they're around). Don't buy too cheap on this; but if you need a bigger stock pot you can buy a very inexpensive stock pot, from Target for instance.
12 qt. is probably what your instructor recommended. It's big enough to handle beef bones, tons of tamales, lobsters, what you will -- but with a diameter of less than 12". A 16 qt stockpot is 13" and you'd be surprised how the extra 1-1/4" will take over you stove. An 8 qt is a little small size for beef and veal stocks, particularly. They're enough of a PITA to make, it's worth making more than a gallon at a time to have and store (if you have the freezer capacity, of course.)
When I actually make beef stock, I use a quart and a cup to make espagnole, (reduces down to a quart), use a cup of the espagnole to make demi, and freeze the rest. I save 2 qts of stock in the refrigerator for soup for soup and sauce making (using a cup of stock to make the demi that day), and freeze the other 2 quarts. The stock disappears pretty fast, actually.
Since I know you're going to ask:
QUICK (HAH!) ESPAGNOLE
3 tbs butter, divided
1/2 cup onion, medium dice
1/4 cup cup celery, medium dice
1/4 cup carrot, medium dice
1-1/2 tbs flour
1-1/2 tbs tomato paste
5 cups veal or beef stock, divided
1/2 bay leaf
3 parsley sprigs
Melt half the butter in a pan over medium-high heat. Add the mirepoix and cook until the celery and carrots are tender, and the onion browned. Add the remaining butter, and as soon as it melts, add the flour. Reduce the heat to medium low. Stir the flour, butter and onions together. Continue stirring until the flour begins to take on a caramel color. Push the roux to one side of the pot and add the tomato paste in the center of the pan. Allow it to cook undisturbed for a minute or two. Raise the heat back to medium high and stir the roux and paste together. Keep stirring until the paste's color darkens and it no longer smells raw. Add 1 cup of stock and deglaze the pan. Allow the sauce to come to the boil and whisk to form a smooth, thick paste. Whisk in another cup, and allow to come to a boil, then whisk in the remainder. When the sauce boils, reduce the heat to a simmer. Reduce the sauce slowly by about 25% whisking occasionally. Pick out the bay leaf and strain the sauce through a fine sieve. You may press the juices out of the mirepoix if you desire. Reserve. NOTE: This is a "mother" sauce. It's useful for a lot of things, but lousy on its own. Don't believe me? Taste it.
2 cup espagnole, as above
2 cup beef stock
Combine the espagnole and stock in a pan. Put on a medium-low flame and bring to a simmer. Adjust the flame to hold the simmer, and reduce by 50%, stirring occasionally. Sieve or tamis the sauce when it's reduced. Reserve 1 cup of demi in the refrigerator and freeze the other cup.
Note: These recipes are off the top of my head. That doesn't show what a great memory I have or anything like that. It shows how fundamental both of these sauces are. Worth learning to make? Absolutely.
If you want to make a great sauce for steak: Take your cup of demi, and add 1/2 cup of stock and 1/2 stock of wine, and bring to a simmer and reduce by 25% and adjust for salt and pepper. Remove the sauce from the heat, and whisk in 3 tbs of butter, one at a time; adding the next piece only after the first has been absorbed. This is a variant on the bordelaise sauce, from which I took my screen nic.