Nowadays, you can buy tickets at the stadium unless is a championship deciding game . Cheapest standing section starts at $80, if you want can get close to the "barra brava" and try to sing along. Nothing to fear as long you don't do anything crazy or start talking gringo. Not sure which kind of experience you are looking for though, as alternative, a cheap seating section is about $150 but think a lot more if you want a good viewing spot.
I'll be going this Sunday night to Racing-River in Avellaneda, about 45 minutes from Obelisco. It's the oldest "clasico" but both teams are not doing so well right now. If you want, we can meet near Obelisco about 3 hours before the game and go together from there. I usually meet with other friends at the "popular/cheapest standing section" as we are club members and don't have to pay for that section. You could go with us (costs $80 plus $50 of an extra fee the club collects, there's also a plain $80 but is on the other side of the stadium) or just buy a ticket for the seating section.