Singer Featherweight
 

Just inherited this featherweight machine. What size needle does this take? I don't know where to find the #, but it's from 1948.

If you are asking about the diameter of the shank of the needle, it's the universal domestic sewing machine needle size, a 15x1. If you are asking about the shaft size, that depends on the material you want to sew. Shaft sizes go from 8 (very thin for fine material) to 19 (very thick for heavy material).
You should Google "The Featherweight Shop". I'm not affiliated with them, but I have 7 Featherweights ranging from years 1935 to 1964. They have an awesome site that's all about Featherweights. Not only can you buy accessories from them, there is a section called "Schoolhouse" that is very informative. I have gotten lost for hours in the articles and videos they have on their site.
Enjoy your machine!

If you just inherited your machine, congratulations. It may not have been used for quite a while. Your machine needs to be seriously cleaned oiled and checked over to make sure that everything is working. I would find some one who refurbishes or someone who can really go over the machine take parts of it apart and clean it, oil it. I bought my featherweight from a lady who does just that. She also showed me techniques the make my machine work. Without any of that you will run into trouble, get frustrated and not enjoy your featherweight. I just adore my machine. It sits in front of me as we speak. My lady pointed me towards the best oils for it. Also the www.featherweightshop.com is where I get my cleaning, oiling, belts, screws etc. They will have everything. Mine is a 1954 Featherweight

I use a regular needle in mine. But go in differently.

Good tip! You should be able to find a free manual online. This will help you a lot. I always make sure they are cleaned and oiled before I start using them. And yes, I use them. I had to have one of the foot pedals rewired -- it was badly frayed.

Love my Featherweight! I hope you enjoy yours as much as I enjoy mine!

I second the cleaning and oiling. My white FW was very clean but dry as a bone and the needle was stuck down. A couple of days of cleaning and oiling fixed that and it's been sewing like a dream ever since.

I used my regular Schmetz Microtex needles in mine. I mostly piece on it so I use 80/12's

Here's a link to the manual. It should answer your questions. Featherweight manual

As I remember, the manual tells you to use Singer needles which really isn't necessary. I don't much like them and find Schmetz needles sew much better (no pun intended)