The houses built in the 50's or earlier may not have a sauna of their own, because in the old days there has probably been a public sauna somewhere close by in the neighborhood. There has been about 100 public saunas in Helsinki, but nowadays there are only few left. Sauna expert friends of mine took me to Hermanni public sauna, which is a small, cosy and maybe not that well-known public sauna with a gentle electric stove. Kotiharju sauna with wood stove is bigger and more popular among tourists, and sauna Arla is famous of its gas stove.
I warmly recommend to try a public sauna, it's a living piece of urban history in Helsinki. I can't think of any other place where people would be more equal than in public sauna: sitting and sweating naked in dark heat, side by side regardless of your background, income or opinions. That's an atmosphere you simply can't sense by reading a guidebook.
One-time ticket is around 10 euros, beverages cost couple of euros a bottle. You can bring your own towel but they also borrow towels for couple of euros. There are back washing services available, but you need to book that in advance. The real hard core adventurists may even try out kuppaus, cupping.