The crux is, for outside, it depends how much power you really want and if you're prepared to pay for it.
Received wisdom is that you'll need 600Ws to 'overpower' midday sun.
That's either one 600Ws head, a couple of 360's, 3 200's or 6 general purpose speedlights.
If you are happy to reduce your need to 'fill' in bright sun, you can use a speedlight.
But my advice would be to go for at least a
Godox AD200 as a flexible start point.
You'll also need a stand, and a
softbox and bracket. You can get away with an umbrella, but as a first light modifier, a softbox is the easiest option.