If I was just starting out, and buying Snap-on on student discount, I would buy the following from Snap-on if I couldn't find a deal on it used first:
Set of 1/4" drive sockets, regular and deep metric, shallow only SAE.
Set of 3/8" drive sockets, shallow SAE.
Set of 3/8" drive sockets, regular and deep metric.
Universal joint, 3 extensions from 2 to 6 inches for both 3/8 and 1/4" drive.
1/2" breaker bar, 2, 4, 6 and 10 inch extensions and reducer to use with the 3/8" sockets. (look for used 1/2" drive sockets in good brands, you'll need them eventually)
Set of metric combination wrenches, 6mm through 19mm.
Ratcheting screwdriver.
Set of flat screwdrivers.
I would look for a used deal on everything else, or buy it as I needed it, shopping among other brands as well as Snap-on. The key thing is to buy as much as you can of what you need, in a quality that will work for you, at the lowest possible cost, and preferably without going into debt for it. If you can get your basic tools up front, then money you make with them can be used to buy tools to speed you up or make your work easier or safer.
The thing I would not buy snap on immediately is my ratchets. I would get a basic ratchet used in each size to use initially. Used, you can get great US quality ratchets for $10 to $15 apiece. Then, try every ratchet you can get your hands on and see what you like before you make an expensive purchase. You'll use your ratchets a lot, you'll want to get what works best. I have several snap-on that sit in my box unused; there's others I prefer over them, as well as some snap-on I prefer over other snap-on. That wasn't as obvious to me when I bought the snap-on I don't use, but became apparent as I used them.
There is plenty of time in a working career to acquire prestige tools. After working for awhile and seeing other techs tools, you will know a lot better what you need and want to pay premium prices for.
What I have arrived at over time is that the following is worth paying Snap-on premium for:
1) 1/4" drive ratchets, extensions, sockets.
2) 3/8" drive sockets.
3) Ratcheting screwdriver.
4) Screwdrivers and picks of any type. (they work better plus you'll warranty them a lot, so the warranty & convenience is important)
5) Torx sockets
6) Hex sockets (I also like Proto really well).
7) Flare nut wrenches
I also really prefer the following in Snap-on, but like others also such as Proto, SK, Mac and Wright:
1) 1/2" drive sockets, extensions, etc.
2) Long combination wrenches
3) Long DBE wrenches
4) Short combination wrenches
5) Swivel sockets
On this above list, the ease of warranty in a shop might tip the scale to snap-on.
Things that I don't see an overwhelming advantage to Snap-on in the tool quality are:
1) Pliers. I only have a few; all the others are Klein, Knipex, Channel-lock, proto, Xcelite, etc.
2) Hammers. I have a couple of dead blow or rubber face, but most of the rest of mine are other brands instead.
3) Electronics. You pay a premium for Snap-on and don't necessarily get better. Convenience in a shop and support may make them worth it.
4) Impact sockets. Lots of others just as good for half the price.
5) Air Tools. Better ones out there for less money. No warranty or service advantage.
6) Taps & Dies. Snap-on are real good, but are disproportionately expensive. Again, warranty advantage might make it worthwhile.
7) Torque tools. On the fence on this one; I have Snap-on and others, but no preference.
8) Punches and chisels. Good, but expensive. I prefer Starret for quality, others for lower expense. I have Snap-on, but have many others. I only have the Snap-on because I found used for cheap.
9) Hex keys. Many other good sets, and see no quality difference for the huge snap-on price differential.
10) Saw blades, drill bits, and other expendables. You pay a lot for Snap-on convenience, without them being appreciably better.
11) Power tools. Essentially the only benefit they provide is that they deliver to your shop. So does UPS, and you can buy for a small fraction of the cost online and ship to you.
12) Tool Storage: Their boxes are nice and carry a lot of prestige. Used or less expensive boxes carry the tools fine, but don't carry the prestige. I'd wait on the prestige until I was making a lot of money and knew I was in it for a long haul.
13) Pry bars. - Shop around, not only for price but for what you prefer.
14) Gear pullers, bearing presses, bearing drivers, etc. - Shop for what you need that works best. Snap-on might be a big part of that, or none, depending on your needs/preferences.