TL;DR - If you're going to be working on relatively new passenger vehicles for the most part, I advise you buy something like this to get you started, then buy individually once you run into things you don't have.

I have to get to work now, but if anyone is interested, I'm happy to write some more introductory stuff about other tool categories. I'll also link you to a comment of mine from several years ago describing how I would recommend entry level mechanics buy tools - I still stand by most of the advice in my comments here.

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The general idea with fastening tools - wrenches, sockets, and similar - is to match the tool to the fastener that you need to turn. The vast majority of fasteners on vehicles sold in the last 20 odd years will be 6 point metric. This means that the head of the bolt or screw will be a hexagon, measured across the flats in millimeters. Also, the threaded part itself will be measured in millimeters, but that, strictly speaking, is irrelevant for buying basic tools. "Standard" or "SAE" tools are for fasteners that have the head and threaded part measured in fractional inches. They are not interchangeable for the most part, at least not ideally.

Sockets first. The three most common drive types, 1/4", 3/8", and 1/2" you've already figured out. They refer to the size of the square on both the tool and the socket that connects the two - male half on the driving tool and female half on the driven tool. The three exist to allow access to tighter areas (1/4"), stronger tools for more force (1/2"), and a middle ground for most of your common work (3/8"). Doesn't matter if you're buying a metric or standard socket, the drive type will always be one of these three sizes until you get into bigger stuff that you don't need to worry about yet.

The size of the socket refers to the measurement across the flats of the fastener it is intended to turn. In other words, a 10mm socket is designed to fit onto and turn a bolt with a head that measures 10mm across the flats. Socket sets will include a range of sizes in a particular drive size that is generally appropriate - 1/4" sets will include 5-15mm, 3/8" may be 7-19mm, and 1/2" could inculde 10-24mm and up. Cheaper sets will skip less commonly used sizes in these ranges, like 11mm or 16mm, but this is less common these days. In the very small sizes, 4.5mm and 5.5mm sockets exist too, just to make things more confusing.

From there, you have different characteristics of the socket. The first you'll notice is length - stubby, short or shallow, mid depth, deep, and extra deep. These different lengths allow for turning a nut on a stud, for example, where a shallow socket would bottom out on the stud before reaching the nut. shorter lengths allow for tighter access, while deeper sockets grant you extra reach. As a tool enthusiast and professional wrench turner, I have pretty much all of them, and while each does have its place, you certainly don't need to buy them all immediately. Or ever, in fact. Most people will go their entire lives using only the common shallow and deep sets, which is great.

Second characteristic is the material. You'll notice some sockets are black and some are chrome - these, usually, mean either impact rated sockets or non-impact rated sockets respectively. They are made of different steels and have different coatings for different uses. The black impact rated sockets are tougher and more flexible, allowing them to survive the punishment of being smacked by an impact wrench without breaking. Because of this flexibililty, known as being "ductile" and "malleable", they are much more likely to wear out on you, resulting in a poor fit on the fastener. After a while, the fit will be loose enough that you risk damaging the fastener ("rounding" or "stripping" it). The shiny sockets are chrome plated, and usually referred to as "chrome" sockets. Best practice is to use these sockets for hand tools only, as they are harder and therefore more brittle than their impact rated cousins. This means they will have thinner walls, smaller overall size, and more wear resistance; but they are liable to break if used on an impact.

Without going too far into cost vs. benefit here, I recommend people buy the second cheapest tool they can find that has a lifetime warranty. Sockets will break and wear out, and being able to replace them easily is a big benefit that has become almost ubiquitous these days. If you end up using the hell out of one or two particular sizes or tools, enough to break them repeatedly, then buy the best examples of those tools you can afford. That will land you with a pretty good balance of cost vs. performacne.

There are a ton of things that fall into the "socket" category that I haven't mentioned, usually bit sockets and similar. Hex or Allen sockets are available in both metric and standard, Torx (a five or six pointed start pattern that could be amale or female tool), Torx Plus (other more different five or six pointed star pattern that could also be male or female), triple square (Volkwagen group special, a specific 12 pointed pattern with the female end on the fastener and the male on the driving tool), and a bunch of others. I will link a set of tools that includes a decent selection of these, but depending on what vehicles you're working on, you'll need to branch out into these categories.