My main question is: what's the best HO Big Boy manufacturer?
The answer to that question is easy, but requires a long explanation. The answer is Trix / Marklin. Trix and Marklin are the same model except that Trix is the made for USA model with 2 rail power while Marklin is their standard 3 rail design. The hard part is finding them since they have not been produced since the early 2000s. Normally I would not have even mentioned the Marklin model, but two reasons. First, I see that you are from the UK and Marklin is probably much more common over there than it is here in the USA. Second you said "outside". Outside and HO don't normally go well together, but the Marklin 3 rail studded track might work better outside.
I want something with nice slow speed control. From what I've seen, the Rivarossi seems to be smooth on start up.
All Rivarossi are not created equal. The Big Boy made by Pocher starting in the mid 1960s through the 1980s was sold in various versions and under several brand names including Pocher (in Europe), Rivarossi, AHM, and IHC. The line was sold to Hornby models in 1981. These early models are not nearly the quality of the Rivarossi version that was released by Hornby under the "Rivarossi" name in the 1990s. I believe that Hornby is still producting a "Rivarossi" Big Boy but I don't know if it is the same or a yet newer version. So the bottom line is that the newer the Rivarossi model the better. I do not recommend the original design as they had some issues with gear boxes and valve gear binding. The first part was easily fixed with a set of gears by Northwest Shortline but once again more expense and work effort spent on a so so detailed locomotive.
Other non-brass manufacturers that would be a better model in both detail and running quality are:
Broadway Limited Imports, BLI for short, (I think 3 different versions) Paragon, BlueLine, and Paragon 3.
Athearn Genesis
And I hate to say ...
Mikes Train House, MTH for short. I personally refuse to do business with MTH because of their corporate behavior and ethics issues.
While I don't specifically own any Big Boys by these companies I have many other steam locomotive models (including Challengers) by Broadway Limited and Athearn Genesis. I can recommend them as a brand in general.
Next, what wagons (cars?)? I'm assuming box cars and tankers etc. How do I tell what's proper period equipment? I need a long train as I'm building a garden layout. How many cars to look good without overpowering the locomotive?
All USA freight cars have a build date painted on the side. They also have rebuild dates. So as long as that date is less than 1959 it would be prototypical. Most prototypical common dates would be less than 1951. Basically any standard 40' box, flat, open hopper, tank would work as well as ice hatch reefers would make a good prototypical train for it. Avoid covered hoppers, center beam lumber cars, and other specialty cars.
Length of train will depend on the specific model of the locomotive you get, any curves and grades on the track. Prototypcially a Big Boy would pull a very long train.
but I can run HO with more realistic curves.
For your information - the minimum curve a real big boy can turn is 20 degrees, which comes out to about 40" radius in HO scale.
https://www.steamlocomotive.com/locobase.php?country=USA&wheel=4-8-8-4&railroad=up#346
Models can turn much sharper than that.
As stated above, outside and HO don't usually mix well, but it has been done. It is hard to keep the track clean enough for good performance inside, let alone outside. For that reason, you might want to consider a battery powered control system for the train.
Hope this helps.
