Hi Gary,
Yeah this got me wondering when I started out, now I'm just a little way ahead of you on the learning journey (I'm no expert!), I'll share my thoughts, but hope members with more portrait experience will also advise.
It depends, to an extent, on how big your home studio room is?
Please tell us, including height of ceiling (I note you are in UK, but you could be in a high ceiling Victorian or Georgian house, or something more modern and compact).
Also whether you're hoping to shoot full length (i.e. standing adult) poses or just sitting?
Another factor might be whether you're talking of just one subject, or small groups?
For a modifier to be effective at producing soft light on your subjects, you want it to be closer than twice its diameter when you light the subject.
You also want to be able to have it above your subjects, to avoid 'uplighting' them too much (from its lower edge). So depending on your room's ceiling height, that may be the deciding factor on diameter.
You'll note they are conflicting requirements
However, another thing to bear in mind is that depending upon the wall colour and proximity to subject, if you use shoot through umbrellas in a room with pale nearby surfaces, the light will bounce everywhere; off walls and ceiling and filling shadows when you might have hoped for a greater contrast. This is why, particularly if your space is small, soft boxes or reflective umbrellas will be a better choice.
I only bought cheapish, off Amazon UK.
Initially I bought one white shoot through, about 33 inch diameter, which I rarely use.
I now have two identical 40 inch reflective white/silver umbrellas for use as main and fill.
So far my subject has been a grand daughter, shot at floor level, so they've not hit the ceiling yet, but they would if I tried to shoot an adult standing.
I also have a 24" soft box, the problem is, only one and it's a bit of a pain to erect and dismantle, so it stays up, taking up lots of storage space!
I wish I had a cover to turn the reflective umbrellas in to a pseudo soft box and help eliminate the 'segmented' catch lights in eyes. I shoot so rarely I haven't sorted this yet.
I do recommend buying in pairs (of whatever), I will in future.
Hope that's helpful,
Dave