CIG are now a brand of welder, BOC is who you want for gas but I recommend Supagas, an Aussie company that are good to deal with.
Also check out Air liquid and
There is another brand but the name escapes me now, they used to be Linde and they now have a new name (another takeover I think)
Beware of Air Liquide though, they have a shonky system wherein they charge you a penalty fee if you don’t exchange the bottle every 3 months effectively making it double rent, it was the main reason I pissed them off.
For heating, brazing, cutting and silver soldering LPG works fine and yes your barby bottle would be the best deal, it’s what I use but you will still need a bottle of Oxygen to run with it.
It’s not much chop for fusion welding though as setting a neutral flame is either hard or impossible, I gave up last time I tried.
Those little bottle things sound like they might be the go for small jobs but I wonder what sort of heat you get from them,?
Never tried them myself but I have an LPG soldering iron that runs without an oxygen bottle and it doesn’t put out as much heat as a system that uses an oxygen bottle