2x3" sheet film is a bit narrower than 120, so it won't normally fit on a 120 reel.
The Nikor sheet film tank is adjustable to all sizes down to 2x3". The Yankee tank will do it as well, but I don't care for the Yankee tank. There are also tanks and hangers, but for some reason, it is very easy to find 2x3" filmholders (I developed a huge surplus at one time as people seemed to be giving them to me with other things, when they found out I was shooting 2x3"), but it is not so easy to find 2x3" hangers. It took me a while to develop a collection of them.
I've done it in trays, and it is pretty easy compared to larger formats.
Very old film will likely be foggy. I've played with some of it (search on "film archaeology" to find the thread where I've discussed my experiments with ancient film), and it's kind of interesting for the sake of knowledge, but it's not the best way to make good photographs.
The best film option is to wait for the Ilford special order period and get some FP4+ or HP5+, but bear in mind that special order 2x3" film from Ilford is about the same cost per sheet as 4x5", which is available off the shelf. I'm not sure which of the East European manufacturers are currently cutting 2x3", but I've used Efke 100, which I like, and I think some of the Foma films are available in 2x3".