I've just recently found Handmade Hero and am currently following along at home using the YouTube archive (I've done the Intro to C stream and am up to Day 6) and I was looking for some advice.
Simply, my goal is to learn how to code games.
I have extremely limited programming experience (Only messing around with drag 'n' drop on Game Maker) and am wondering if solely doing this series is a good idea? Should I learn C individually by itself first, or perhaps do both simultaneously?
this series is not intended to teach you basic programming. In my opinion you need to have at least some programming experience in a programming language. The streams mostly focus on more abstract concepts which are required for programming games (e. g. memory management, optimization). If you are just starting to learn programming these concepts may be too abstract and you won't be able to undestand why these things are relevant.
I would suggest you try to learn C programming by making some very simple games yourself. You can start with simple console (text-based) ones. For example a text adventure or a quiz game. By doing these you can learn the basic control structures of C and how to organise your program code.
But you have to decide that yourself. Maybe try watching some videos and see how much of what is happening you understand. If you are not able to follow what's happening in the code then you should consider going back learning more C first.