... I'm not sure I want to spend that much money on lighting - I'm not planning to do anything serious with it - but thanks for all your recommendations.
Just saying. Flash can be far more transformative to your photography than a new lens. It might make sense to budget accordingly. $200 is peanuts compared to most photography equipment. And the pieces I mentioned are the bare minimum at the lower-end prices. A $25 Amazon Basics flash will be manual-only, won't have a built-in radio trigger (so you'll have to probably pay another $20-$40 to add one on; at which point the $65 of the TT600 looks pretty similar), and its build reliability might not be so good (a ton of 1-star reviews on Amazon mention the flash tube blowing quickly).
In 2006, it used to cost you $200 just for the radio triggers and they never came built-in.
As for the speedlight, would you recommend buying a softbox or other diffuser for it?
Well, a softbox is going to easily cost double what an umbrella would. (Say, $45-$60 for a cheap Chinese-made one vs. $20 for the umbrella). That's why an umbrella tends to be the default recommendation and why I added it to the list of things you need. Again, check out
this Strobist link to see how it all goes together. With a Godox TT600/TT685, you won't need the radio receiver, because it's built-in. You could try starting out with a tripod instead of a lightstand; as long as the swivel/adapter comes with the spigot, it'll attach to anything with a 1/4"x20 thread. But lightstands are better, because light tends to comes from overhead, and tripods rarely go that high. You could
DIY a clamp, but...better to start off with the proper tool.
I do often prefer a softbox to an umbrella because it's easier to control the spill and to use the edge of the softbox to feather the light (create a gradient in the falloff), but. It's just a different look from an umbrella. You kind of generally want both, not one or the other. The main issue is finding out what size you need. A smaller 24"x24" softbox is only going to be good for head or torso shots.
An umbrella can be used either a shoot through or reflective, and is much easier/faster to set up, so it's a more versatile and cheaper way to start out than a softbox.
Modifiers are kind of like lenses: which ones you want depends on what you want the light to look like and what you plan to do.
The only other no-brainer modifier, aside from an umbrella, that I can recommend is Neil van Niekerk's
"black foamie thing", which is a small sheet of black craft foam that you use to flag off direct light coming from your flash when you
bounce (i.e., aim the head of the flash at a reflective surface and use that as your light source for a softer/more diffused look). Costs about $1 at Michael's for the sheet of craft foam, and you probably already have rubber bands around the house.
