The Kerguelen Islands could be a pretty interesting place to colonise. It has coal and offshore oil, useful vitamin C containing plants (Kerguelen cabbage) for early sailors, potential to naturalise other plants of value (
Drimys winteri, used for furniture, musical instruments, and other fine woodworking, plus potentially a spice), and endless amounts of wind power. It makes a great base for Antarctic exploration/exploitation (early on it would be a good station for lost sailors), as well as a good waystation between South Africa and Perth. It could be another Iceland, and like Iceland's hydroelectric and geothermal power, Kerguelen has a huge potential for renewable energy as well, especially wind power. If I ruled both the Cape and Western Australia, I'd strongly consider putting at least an outpost on Kerguelen, if only for helping castaways/damaged ships and maybe for Kerguelen cabbage (maybe a dish containing it makes its way to the stomach of some prominent individuals).
Controlling Cape Horn (Tierra del Fuego), the Cape of Good Hope (South Africa), and Cape Leeuwin (Western Australia) could provide interesting advantages (near complete control of the Clipper Route and the Southern Ocean in general), and Kerguelen is one of the places you'd need to control to get there.
All interesting ideas.
Siberia was colonized OTL and at the time it was a pretty wacky place to set up. How many people could Siberia support if we pack it to carrying capacity (just counting areas east of the Urals)? How does the population distribute?
Siberia wasn't any less reasonable than settling the American West. Given that it was rich in furs, the Urals with their noteworthy mines since early on (before mining was extended everywhere), and later being Russia's route to China and the Pacific, it made plenty of sense. Plus remember that Siberia has a ton of farmland along the southern borders of Russia.
The problems with settling Siberia was the Russian system of serfdom and its increasing restrictions over the years, and also the fact that it was pretty damn far compared to Novorossiya and the Kuban. Travelling the river routes is much more difficult than the comparatively easier journey to the southern steppes. Also, in either case, it had to wait until the Russian state could project power into that region against the Turkic peoples (Crimean Khanate, Kazakhs, etc.). But in theory, a "settled" Siberia (maybe with a Volga Bulgaria/Tatar wank) could probably have twice as many people as today. Not entirely sure on that, but with modern agriculture, robust transportation, and early development the region could host a lot more people. Individual parts could probably have a lot more, like a Japanese-colonised (from the 16th century at latest) Kamchatka/northern Sea of Okhotsk areas, or even China pushing north into parts of Siberia.