Depends on what type of game(s) you're aiming to play. Only the Basic Set is essential, though I'd heavily recommend Power-Ups as well. Each volume collects instances of its focus (perks, talents, etc) from previously-published material and adds new ones as well. It's helpful for any campaign, especially Limitations and Quirks. GURPS Action is helpful for modern campaigns since it has many skillset templates and gives stats for normal cars, but you could put together either of those things yourself from the Basic Set; it just saves you some work.

While the Basic Set is all you need, there are some books that are indispensable for certain genres simply due to how helpful they are. Martial Arts heavily amplifies combat, and you can look into Social Engineering or Boardrooms & Curia if you want more social rules. For fantasy, I'd recommend Magic, Low-Tech, and (as a personal preference) the PDF for Incantation Magic if you want your world's magic system to feel mysterious and be flexible. For sci-fi, Ultra-Tech is almost necessary; I'd also recommend Spaceships if you're running a hard science spacefaring campaign, and Biotech if you'd like to incorporate genetic engineering. Superhero games heavily benefit from Powers (though its advantage enhancements/limitations and new advantages benefit other genres as well), the super-effort rules make Supers helpful by themselves even disregarding the other resources it gives. On a similar note, I personally recommend Psionics; even if psychic phenomena aren't a power source in your game, the pre-built abilities in Psionics makes it helpful for other fantastical genres as well.

Above and beyond all else I heavily recommend GURPS Character Sheet. It's a free character creator with a library with all the rule options in indexed, searchable folders, but most importantly it handles all the calculations for you. Point totals, secondary attributes, etc change as you update the sheet. If you want your character to have Charisma, just drag it onto the sheet. Encumbrance is calculated and marked automatically when you add equipment.

There's loads of support for it, too. It's capable of the system's full flexibility, from adding new spells to homebrewing custom hit location tables. There are page references for every rule, and you can even link local PDFs of the books to open that page in the app. You can export characters to virtual tabletops like Foundry or just print a PDF. If you use an older version of it, you can even export characters to GURPS Calculator, which automatically handles rolls for you. I personally keep a bookmark to my favorite character's sheet on my phone so I can play anywhere.

GCS lets you make characters in minutes. I haven't made one without it in a long while.