Bullet

Oh boy - this is a big question.
 
I think many of the photos you have already aren't bad at all. The one with the back end of a dog could go.
 
For outdoors you may not need lighting at all. You are possibly going to run into an issue with the reflective nature of your metal work. Any lights you shine on the subject are going to reflect off it.
 
Q1. A softbox isn't a light; it's a lighting modifier. You probably knew that. Cheap modifiers can be OK. Maybe not as robust as better quality ones. I use an umbrella box which is kind of a half way house between an umbrella and a softbox. A bigger lighting modifier gives you a softer light, as does having the light nearer the subject.
 
Q2. You can get continuous lights. The cheaper ones don't have a lot of power though, and can get hot - so I've heard. Or you can get studio flashes - e.g. Alien Bees or Elinchrome (sp?) which are more expensive. Or you may be able to use a flash gun off camera and stick that in a softbox, or similar. That's the set up I use. See http://strobist.blogspot.co.uk/
 
Q3. You probably want some direction to your light - not just flat on. But how dramatic / harsh you want it is up to you. I'd probably go for softish light myself. Some shadows to look 3-D - but not too harsh.

a good start
 

Guys,
Thanks all for your feedback. I haven't made up my mind yet, I am weighing up all options. Thanks Jane B for the link to the Lmix camera, it is a fair price to.
 
Cheers
Glen

This is bugging me now because I feel that there ought to be other compact cameras that have the features you want. It's just a case of finding them.
 
This has time lapse for example: http://www.amazon.co.uk/Panasonic-Lumix-Camera-LEICA-Summilux/dp/B008N8NZDK/ref=sr_1_1?ie=UTF8&qid=1400753135&sr=8-1&keywords=lumix+lx7 but not sure about remote control.