Start out with what you can afford. You don’t want to be getting out of school owing all that money for tuition, plus another 20-30 grand in tools. When I started out I could barely afford Craftsman, and I didn’t have schooling to pay for. After I changed employers a few times and started working some place the tool trucks actually stopped at, I started upgrading to better tools. I probably spent about 3000 last year on tools.
You can definitely tell the difference in quality from the cheaper ones to the tool truck ones. As far as which brand is better Mac, Matco or Snap On it’s gonna be personal preference. I personally like Snap On ratchets over Mac they feel better to me. Mac offer a lifetime warranty on drill bits Snap On doesn't. There is no right or wrong. It just comes down to what you want to spend, what you want out of it, and so on.
I work out in the field so I don’t want to have to worry that I am going to break a tool and not get the job done, so I feel the tool truck tools are better. On the other hand I have known guys that get everything at Harbor Freight and do the same jobs. It just preference and experience.
And toolboxes, ya they are nice but I don’t think I could ever drop that much money on one. The biggest one that Snap On makes, just the bottom box is like 33,000. I think the wife would kill me if I came home and said "instead of getting a car I bought a toolbox, it was just a little more than a car cost." But my toolbox is a truck so I don’t know.