There are a lot of good suggestions in this thread already. Maybe I can add some thoughts based on running Makerspaces for a few years:
- I've hardly ever seen starter kits used fully. I think this is because most people I've seen have gone from learning the absolute basics (blinking a LED, usually) more or less straight to working on some individual and more complex project. For these, you usually end up needing things not included in a beginner kit (components, bigger breadboard, ...). However, there is nothing wrong with a starter kit and if I had to buy one, I'd go with an original Arduino kit [0].
- There are some really nice education-oriented boards available nowadays that integrate a lot of functionality (RGB LEDs, microphones, buzzers, LED matrices, light / acceleration / temperature sensors, you name it). Somebody already mentioned the micro:bit[1] but there are others as well. I can recommend Circuit Playground Express[2] or Calliope[3], for example.
- You can never go wrong with an Arduino Uno[4]. It's basic compared with newer offerings but in many ways it's a classic (lots of documentation and compatible hardware / "shields" out there). Buy the DIP version if you can, it's more repairable and flexible than the SMD versions.
- There are quite a few ways to code for those educational microcontrollers. Most of the fancy newer boards mentioned above (micro:bit, ...) are made to be used both with Micropython/Circuit Python[5] as well as with Open Roberta[6] or MakeCode[7], the latter two for a more visual approach to coding. Unfortunately, those boards usually are not Arduino compatible which is a shame because the (probably) most wide-spread way to code for educational microcontrollers in general is the "traditional" Arduino IDE[8].
Most people I've seen end up with Arduino compatible boards and the Arduino IDE because it's more flexible and most of the documented knowledge, libraries and other stuff out there relates to that. Of course there are other options as well ("modern" alternatives to the Arduino IDE as well as the chip makers' tools themselves, ...) but those can be ignored in beginner contexts.
- For beginner workshops, we often use a Circuit Playground Express for younger or very inexperienced persons (or if we really don't have much time). For everybody else, we most commonly use Arduino Unos with a breadboard, maybe a soldering iron, some jumpers, LEDs and resistors and go from there.
- My favourite supplier by far is Adafruit for a lot of reasons, mainly to do with their open source and hacker ethics as well as with the quality of their tutorials and documentation.
- I make it a point to regularly buy from Arduino (as in https://arduino.cc - not the clones) because their stuff is good quality and it's well worth supporting the "original".
- Seeed Studio has also been mentioned and I think it's one of the coolest companies in this space. You can get a lot of more exotic and specialized (and cheap) stuff from them as well as all the basic Arduino things. They are also a manufacturing & development house (PCBs, assembly, CNC, 3d printing, ...). However, in my experience, their documentation and tutorials are not as good as with Adafruit, Arduino or Sparkfun.
- I can highly recommend TinkerCAD Circuits[9] as a secondary learning tool. It's a pretty awesome microcontroller playground / simulator / learning space. Unfortunately, AFAIK, there is no real open source alternative.
[0] The traditional choice: https://store.arduino.cc/products/arduino-starter-kit-multi-... -- however, I think this one is more practical: https://store.arduino.cc/collections/kits/products/arduino-s...
[1] https://www.microbit.org/
[2] https://learn.adafruit.com/adafruit-circuit-playground-expre...
[3] https://calliope.cc/
[4] https://store.arduino.cc/products/arduino-uno-rev3
[5] https://learn.adafruit.com/getting-started-with-raspberry-pi...
[6] https://www.open-roberta.org/
[7] https://makecode.com/
[8] https://www.arduino.cc/en/software
[9] https://www.tinkercad.com/learn/circuits