.NET Core Web API is absolutely perfect for this and the fact you already have some .NET experience makes it a no brainer in my opinion. Just get started knock

.NET Core Web API is absolutely perfect for this and the fact you already have some .NET experience makes it a no brainer in my opinion. Just get started knocking out a prototype running locally and break the analysis paralysis, you'll have no end of hosting options to choose from later. You'll be amazed what a 5 dollar a month Ubuntu server from Digital Ocean or similar will handle running .NET Core. Azure is obviously an option too but don't rule out AWS.