It's almost entirely EQ and distortion, applied in various orders (the exact signal chain matters, because EQ after distortion sounds different than distortion after EQ). By getting this right you can simulate any tube amp tone with solid state to a high degree of accuracy.
Sure but it’s only been relatively recently that the modeling and solid state stuff has gotten close. And even then, it’s still not quite right. Also, even a good solid state or modeling amp is gonna cost a decent amount. Luckily, we have more choices than ever, and I even have a tube powered preamp that’s absolutely killer paired with an IR cab response loader.
Close mic it with a SM57 like your favorite recordings probably did. You don't need any fancy room treatment when close micing. Or just run the direct input through an amp sim and cab impulse response. Unless you're going for a 1950s sound where mechanical speaker distortion actually matters, IRs capture the cab/mic sound very well.