You need to understand few thing.
1. Badminton shoes are specificly design for badminton movement pattern. Which is to support lateral movement, rapid & sudden change direction. Doesnt mean you cant play if you wear a running shoes or even a sandal, but you just risk yourself for injury & the higher your level, the more intense the games which mean even higher chance for you to harm yourself.
2. The same with badminton court that purposely design that way to support badminton characteristic. It made from rubber like stuff to improve grip & also soft enough when you fall on it. Imagine if you play on rough concrate. Pretty sure you dont want to do some Superman flight action & land. Other than that, badminton shoes tend to had thin sole for stability thus the court made somewhat thicker & abit soft to reduce impact when doing jump or stomping the ground when dashing. For all that, badminton court not as strong & solid as concrate, so it need soft outsole shoes to balance it if not, the carpet would be tearing apart easily & you definitely dont want to play on broken carpet. It might trip your shoes & end up harm yourself.
3. Expensive or cheap? Its cheap for reason & expensive for a reason. Cheap mean cheaper material, less support, & less stability. Other hand expensive mean higher quality material, better support, & better stability. Depend on your need you might not need the most expensive one but regardless stick with badminton specific shoes. For example, if you are just a beginer, your movement are not so demanding, so the best support & stability wont be any use for you. But if you are a pro, you would want the best support & stability to protect you from very intense & exhausting movement. Or like me a big bear, need good quality support due to my weight.
Hope that help & could give you some insight of what would you want to buy.