Electroforged Schwinn bicycles require a unique seat post, sized 13/16" to fit the seat tube. These frame tubes are small and have thicker walls than many other bicycles, and certainly compared to modern bikes. So a thinner seat post is in order.
One of the other issues is that most of the old, electroforged Schwinn bikes take a smaller seat clamp size than a standard 7/8" clamp. The result is that if you have old Schwinn 3-speed, there's a good chance you'll need some kind of seat post adaptation if you want to use a standard saddle clamp, something akin to what you'd find on a Brooks B66.
A heavy-duty solution is the Porkchop BMX Cr-Mo seat post, running 13/16" in the frame and 7/8" at the seat clamp. This post is over 14 inches long, because it is made for BMX bikes, which tend to have shorter frames. Given the longer length and heavier construction than some of the less-expensive options (for example, Wald post), this is a good choice for the person who needs to extend the seat post a bit, but wants to use a standard 7/8" saddle.
I am using one of these Porkchop BMX seat posts on my electroforged Schwinn Superior from 1950. The seat post lacks a safety ridge, so I advise using a saddle clamp with a safety "notch" in it to make sure the saddle doesn't try to slide down the post. This seat post seems to go in and out of stock, so keep periodically checking Porkchop's website if it goes out of stock. This is a nice option if you want a heavier duty seat post in the size of the common Schwinn 3-speed. The extended length also gives you the option of setting it to the height of your liking.
A second option, is the common Wald brand seat post, against 13/16 to 7/8. The Wald is a flimsier post, though it does indeed have a safety ridge. The Wald is OK if you are an average or light weight rider and you will not be extending the post very much out of the seat tube. But for a heavier rider, or someone with more than an inch or two of extension, you may want a heavier seat post. I've seen the Wald posts bend, usually from a heavier rider on a seat post extended far out of the seat tube.
I use a Wald on my 1960s Schwinn Racer, which is a tall frame model and has very little extension of the seat post.