A little confused about writeable vs non writeable uids and which chip i need?

i appears like a Mifare Classic 1k will do what you want.

What sort of Test equipment do you have?
Mifare Classic 1k gen1a?
Mifare Classic 1k gen2?
Proxmark3?
Flipper?

TagInfo?
MCT?

Looks like you are trying to use a PC, What is the software you are trying?

I’m sure there are tutorials online for this, but we should be able to help you out if you get stuck.