Did the money come from his family? Was he independently wealthy? I known the economy was very different back then but I don't know enough about it, or him to understand. Buying what he did at 22, today seems incredible to me.
His father Thee Roosevelt (Theodore Roosevelt Sr) had inherited a massive fortune, and went ahead and greatly expanded it. This is why Teddy was able to vacation in Switzerland as a child and attend Harvard as a young adult. Thee Roosevelt was largely the definition of an old knickerbocker (old New York money). Teddy was 19 when Thee died and Teddy, his brother, and two sisters inherited the fortune. By the time Teddy was 22, he was ready to spend some of it to establish himself as his own man, in his own house.
So Teddy got his fortune the old fashion way, he inherited it.