Not sure there is really a right or wrong answer to this question since there are so many variables. I have a 19 year old at work that is going through the same thing. He already has a 4 drawer cart from HF. He has some chrome HF socket sets and is going to add more from either HF, CM, Tekton, Carlyle, GW, Kolbalt, Husky, etc. I suggested he look at ratchets from GW, Williams, & Carlyle. Combination wrenches GW, Carlyle, & Tekton. I recommended Knipex dykes and a pair or two of Cobras. Other pliers from Channel Lock, Klein, CM, GW, Carlyle, & Tekton. Screwdriver set from CM, GW, Tekton, Kolbalt and have a couple of bit drivers as well. Get a few ball peen hammers and a dead blow from some of the above brands. Same goes for a chisel and punch set with Wilde added to the brands list.
Once the basics are covered then add more specialized and drive tools for the sockets.
It really depends on how much you are willing to spend on each particular tool. The next step up would be the Industrial brands like Proto, Wright, & Williams along with SK. Sadly, Armstrong would have been in this group but, are gone for at least the time being. Up from there is the truck brands like Mac, Matco, Snap On, and Cornwell. You may find that you prefer a mix depending on price, perceived quality and the feel of the tool in your own hands.