There are lots of choices, I'm drawing
@Scooter into this, as he has a lot of knowledge of them
Hi Ciaran,
First off, it is all fog. If there is such a thing as a "smoke machine", I've never seen one, and you don't want one - you should not use smoke in an enclosed space. Fog though, is perfectly safe to breathe in reasonable concentrations. You cannot colour the fog (by adding food dye or otherwise). If you see coloured clouds in a shot, it's either lit with coloured light, or it is actually smoke from a pyrotechnical bomb - do not breathe this.
The basic workhorse fog machine is one of these for £50
https://www.ebay.co.uk/itm/126439028191
It seems it's impossible to buy one without LEDs on the front these days. If you're shooting with flash, these won't be bright enough to show up in your shots, but if they are a problem, turn them off, or, if it's not possible to turn them off, open the machine and snip the wires to the LEDs. 900 to 1200 Watts is a good ballpark for the heater, as you can run it on a domestic socket, and will reheat in about 30 seconds. More powerful fog machines don't typically give you more fog, they just heat up quicker. The 400Watt unit Tim linked to will also be fine - it will just take a while longer for the reheat cycle to complete. One advantage of a lower powered heater though is that you could run it off an inverter/battery pack such as the LP800 for use away from mains power.
This is the fluid you want:
https://www.ebay.co.uk/itm/333133382641
I know it says on the container that it's heavier than air when vaporised, but this is a lie. It won't, as they claim, give you a "dry ice effect". It is the most dense fluid though and if you do want a cloud/dry ice effect, you just need to push the output of the fog machine through a piece of 120mm diameter collapsible heating duct filled with about 8 large freezer blocks. It'll stay on the floor for a minute or so, unless it contacts a heat source (such as a live human) in which case it will start to rise and coil around the heat source.
You need to light fog from the back (upstage), to see the structure, or from the side to create solid looking clouds.
This is backlit chilled fog:-
View: https://www.flickr.com/photos/owenlloyd/53593113797/in/dateposted-public/
I had 3 blue backlights in this shot, left, centre and right.
In the studio, make sure all doors and windows are closed as even the smallest of spaces will have its own air currents and your fog may not go where you intended
Fog is also essential for showing laser patterns
View: https://www.flickr.com/photos/owenlloyd/50484071621/in/dateposted-public/
Here's the fog video I made a few years ago
https://www.youtube.com/watch?v=TyQkJZuhGos