Hi Katie! I'm sorry that you're having trouble with your Nikkormat FT3 and hope that I can help!
First of all, 50mm is the focal length ot a particular lens, it has nothing at all to do with the name of the camera body which is just called a Nikkormat FT3 in this case. The lens you have mounted may be a 50mm lens but you can also put numerous other lenses on this camera.
I do not recommend that you buy cameras from the Goodwill, Craigslist, eBay or any other non camera store unless you know how to assess their condition very well and/or are willing to pay the additional $150 it will cost for a complete overhaul of the camera. $16 is a great deal on this camera and lens if they work but was a waste of money if they don't and you cannot afford the repair cost. Actually, the lens alone is probably worth much more than $16 and is probably working fine so you have probably come out on top with that alone (a lot of probablys but this is good). In the future, buy from KEH.com or other quality used camera shop. You'll pay more up front but you'll have a working camera.
What exactly do you mean by "won't work"? Does the meter read-out on the top and inside the camera move at all? If it does but is apparently incorrect, you may simply eed to refer to the users manual here:
http://www.butkus.org/chinon/nikon/nikkormat_ft3/nikkormat_ft3.htm
If the meter read-out does not move at all, a couple things could be going on:
1--The battery needs to be the correct type, a 1.5 volt LR44 or A76 type battery. It also needs to be installed correctly with the plus side of the battery facing the battery compartment cover where a plus symbol is engraved. You can also rub a pencil eraser on the battery terminal, inside cover and battery contacts to clean them and be sure you're making a good connection.
2--The light meter needs to be activated by pulling the film advance lever out slightly away from the body, revealing a red dot on the body to indicate that the meter is turned on.
3--In order to see the needle in the meter read-out move, you must then set the ISO, shutter speed and aperture for reasonable settings for the type of light you're pointing the camera at. It's easiest to point it at a window on a sunny day with the ISO set to 400, shutter to 60 and now you can change the aperture back and forth and the swing needle should move.
If the meter is still not showing any signs of life, the camera will need to be looked at by a professional camera repair technician. Start by looking for one in your local phone book or Yellow Pages. If you cannot find one, I've had luck with my Nikkormat at CameraRepair.com.
You say you don't want to put too much money into it but here's the deal. This is a vintage camera and nobody builds cameras of this quality anymore aside from maybe Leica who charges about $5,000 for the favor. So by comparison, the typical $150 for camera service is REALLY CHEAP! Even if you bought a new Nikon FM10 which is made of plastic, it costs over $300. Many people will tell you to just buy another camera but any vintage camera you buy at a low price will have problems so you may as well take care of this one so you have a warranty and know the history of it.
The FT3 is a GREAT camera and capable of amazing photos and once serviced, it will last for DECADES! So if you want a good 35mm SLR, I think the choice is simple!
As has been suggested, you can guess exposure or use a handheld meter with this camera. It does not require a working meter to operate like other automated cameras. So you could do this too. But then again, I bet your FT3 also needs new light seals and shutter calibration. The lens might also need cleaning. Who knows until you hand it over to someone to go over it all? Btw, DO NOT buy a light meter from a thrift shop as qrt suggests, buying camera equipment from thrift shops is how you ended up with a camera with a questionable meter and probably other issues. Suggesting you buy a light meter from the people that potentially sold you a broken camera makes no sense! Again, buy from KEH.com or buy a new meter if you like.
I hope you invest some money into your FT3 and enjoy it as much as I enjoy my Nikkormats. I own several and they are some of the greatest cameras I've ever used. Here are some photos that I've taken with mine:
http://www.flickr.com/search/?ss=2&w=25579835@N00&q=nikkormat&m=text
Please feel free to email me at JohnnyMartyr@Hotmail.com with any questions!
METAL AND MANUAL! FILM FOREVER!