Find a light/system with the following characteristics:
- flash head with a removable reflector (for use inside softbox)
- flash head with minimum 150W modelling light (to see the lighting even in a bright room with sunlight)
- adjustable power output, and adjustable modelling light
- for heads used inside sofboxes, it is beneficial for them to be fan cooled to help exhaust hot air out of the softbox
'Bargain' lights tend to skimp on the power of the modelling light (under 150W), and unless you intend only to shoot in a darkened room, their modelling lights are close to useless when sun is coming in the windows of the room. You need to see how your lights fall on the subject to optimize their positions...otherwise you are merely 'illuminating' the subject and not 'lighting' the subject, to complement their features the best.
There is a traditional debate about 'power pack + heads' vs. 'monolight'. That is an individual preference. You can find Stickey threads on POTN on the discussion topic.
When shooting typical portrait, a starting setup is either the combination of
- one reflector head (main) and one head [Bounced/in softbox] (fill), or
- one head in smaller softbox, with second head bounced/in medium or larger softbox (fill)
The above is 'the basic' needs. Develop your lighting skills first, before going for things like beauty dishes or parabolic reflectors or ring lights, which are a bit more 'specialized' in use. If tight on budget, you can make do with a white foamcore panel to bounce light as your 'fill' light.
The 'danger' of using a 'too large' softbox is that it bounces an excess of light from the ceiling, losing your control of light. Another 'danger' of too large a softbox is that it more quickly hits the ceiling and (when desired) limiting the high angle it might be aimed from.
Amateurs are tempted by the low price of umbrellas, rather than softboxes...umbrellas lose your control of light more than softboxes. They do have a place in your inventory, just realize their fundamental limitation over setting a light in softbox.
Get yourself a radio transmitter/receiver set to wirelessly trigger the lights from camera position, regardless of where they are located in the room.
