If you're going to write a website, there is absolutely zero reason to not use an existing framework. Frameworks will take care of 90% of the work, leaving you able to focus on what the website
does instead of how it's implemented behind the scenes. You cannot afford to be wasting effort on reinventing the wheel, especially when you're short of manpower to start with. And a good framework will still give you a ton of flexibility in terms of picking e.g. what type of database to use and how to scale the site, so you won't be sacrificing control over anything you actually care about.
What specific framework to use...I don't have the necessary background expertise, except that I'd say in general to avoid PHP, despite its wide support, because it is famously
fractally bad. I've used Django (which is based on Python) in the past and been perfectly happy with it. I have never heard of a C# web framework; such may well exist, but I'm not aware of them.
My inclination is to say that writing a website is different enough from writing an emulator that you should care more about using the best tools possible than you should about using a language you are familiar with. Whoever works on the website will have a lot of learning to do anyways, and their code will not (should not!) end up looking very much like the code in BizHawk. That said, it would be good if you had access to someone who is familiar with the language, so they can help advise others and smooth over any learning "humps".
