While I was doing the "free 30 days + 12 months of free stuff", a certain level of MSSQL was listed as free, but hidden under that is creating the storage for MSSQL which is a separate and additional cost that you cannot avoid. (At least, not that I could figure out.)
By the end of my 30 days, I found the bare minimum performing low volume .NET + SQL on Azure was going to be $30+/month even for just a prototype/development site, and I can pay less elsewhere for higher performance (though perhaps less control). And when I say "performing", I just mean the VM not being too slow to actually use as a UI, and throwing low memory errors constantly. The free tiers for Windows Server are, in my opinion, unusable at all.
I run a hobby .net core website on a $5 digital ocean instance and it runs fast as hell. You definitively don't need to spend $30. I'm using a PG database but it looks like maybe it would even be possible to run SQL server on a 2GB instance.
You do get some free storage with the free tier database, but it is only a paltry 32MB. Additional storage is only $0.221/GB/m though. The paid cheapest SQL database (B0) is only $5/m, which comes with 2GB of storage. In practise, this is absolutely fine for light usage.
By .NET + SQL, I assume you mean you were using an App Service? They come with a lot of convenience, but I definitely agree that they are too expensive, especially when considering the level of compute you get. I raised this with someone from Microsoft before, and they said they were confident the value offered was worth it.
There is a free tier for App Service though. It's a shared compute model - I tried it a while back, and the performance was totally fine for light usage.
I wouldn't try to run Windows Server on a B1S, as they only have 1GB of RAM :) You might just about get away with it for Server Nano, but I've never actually used it. Best stick with Linux or BSD for these tiny VMs.