Just so others know, cast iron does not have to be expensive. I have 8 cast iron pans and my favorite and best ones have all been found and acquired for no cost. I have a few specific ones i purchased (griddle, enamel coated pot).
Found pans usually look horrible and unusable but with a little work they will be the best pans you own and last forever. Look at yard sales, estate sales, community cleanups, scrap bins, grandpatents basements or attics.
I used to do this at flea markets a few years ago. Find they nastiest, rusted cast iron I could find and then restore it to use in my kitchen. It's really easy and doesn't cost hardly anything to do. I have close to 10 really nice pieces cast iron cookware in my kitchen now.
Assuming it isn't too pitted, you strip it of the rust or old seasoning (the black stuff), then re-season it.
For stripping, I've used the self cleaning cycle in my oven and my big green egg, but don't recommend that as it can cause the cast iron to crack sometimes. I've seen people spraying their cast iron with oven cleaner and placing it in a garbage bag in the sun for a day or two. It's supposed to work very well, but I haven't tried it.
For seasoning, I like to rub a very light coat of oil into the entire surface of the cast iron (get an oil with a high smoke point, I've used peanut oil most of the time) and then wipe the oil off until you can see it anymore. Place the cast iron into the oven and set it to 500F. When it get's to temp let it sit in there for an hour, then turn off the oven and let it and the cast iron cool completely. Rinse and repeat as many times as you want to (I usually do at least 6 cycles to get the seasoning nice and established, but I've done as many as 12 and don't really see too much of a benefit). There's tons of different methods for seasoning cast iron and some people swear by different oils, grapeseed, flax, bacon, vegetable shortening. I've tried a couple different ones and haven't' seen a noticeable difference.
Then you just cook with your new cast iron. After every time, gently clean the pan, then oil it extremely lightly and heat it to completely dry it before storing. Don't cook anything acid like tomatoes, or you will see your hard earned seasoning stripped away in a heartbeat.
I'm sure you could, people use vinegar to remove rust from iron all the time, I've just never personally heard it being used in this application. If you try it though, let me know how it goes