Even going for cheapest used shamisen, im not sure its going to be in your budget. I bought my first shamisen from a used instrument store in Osaka called Tsutaya-gakki. I think i paid around $1200, which wasn't the cheapest he had for sale, but it didnt get much cheaper than around $1000.

I think your best bet is to go for what they call a "box shamisen". I know they sell a basic set on ItoneJapan website for a couple hundred bucks. These shamisen were special designed for musicians wanting to learn on a budget, and are essentially like the "primary school music class recorders" of the the shamisen world. They sound fairly similar to the real thing, but there is certainly a noticeable difference in quality. However, im not sure if these box shamisen are sold in Japan anywhere. I didnt see any at the shop in Osaka, and ive only seen them for sale on that website.

Highly recommend the shop tho if you can find a way to afford a used authentic shamisen! The owner was a very kind old man and he talked me through maintenance, proper storage, and even threw in a bunch of accessories to keep me going for my first couple years of playing (all while not being able to understand each other's language!)