Yes, you need an ZX Spectrum Emulator. Let me give you a sugestion: donwload FUSE http://fuse-emulator.sourceforge.net/
Read Fuse readme file to know how to configure it (Tip: after open it use F9 on the keyboard you can chose the ZX model to emulate, choose 128k model to have in game music).
For using USB controles I recommend using a program like JoytoKey: https://joytokey.net/en/download
You can map imputs form the keyboard to your Joypad imputs. This is the easy way to do it, i use Joytokey in a lot of situations like Old PC games or emulators for old systems that do not have joypad or have complicated joypad suport.
I hope to have helped you, have fun.