Hi, mainly people really.
Do you mean studio-style portaits? In which case Simon/Juggler's advice is dead right. If you have mains power, studio heads are way better - fast recycling (you may be surprised how important that is with portraiture), a modelling lamp so you can see what the light is doing and learn faster, and plenty of power when you need it.
Lencarta Smartflash-2* is a very good little unit for about £110, plus spill-kill reflector, stand, white reflective umbrella, and a white/silver reflector. Loads you can do with that - good lighting is more about knowledge (of how light works) and experience than expensive kit. Umbrellas are just as good as softboxes nine times out of ten, easy to put up/down, make better use of limited floor space, and very cheap (the ones for a tenner are perfectly good
https://www.amazon.co.uk/dp/B00MPHDMQA?psc=1). Then get silver and shoot-through umbrellas - silver gives a slightly punchier light, shoot-throughs are softer when used in a typical domestic environment - light radiates 180 degrees from the front, about half of it bounces straight out of the back, and all of that 'spill' bounces around the room and is reflected back off light-toned ceiling and walls, lifting the shadows).
*Uses the Bowens/S-type fitting for light modifiers - hundreds of attachments available. There are plenty of other heads available, most of them perfectly capable, but nothing better value than the Smartflash-2.