What are Av2-Series and B-Series VMs in Azure? What other VM types are there?

The Av2 series of Azure VMs are suited for entry level workloads like Development and Test. Proof of concepts can be run Av2 series VMs.

The B-series of Azure VMs previewed in 2017. 

They are adapted for bursty workloads such as web server that uses very little CPU until some particular request comes in. 

While not utilizing the baseline performance of the CPU, the VM builds up credits.  

When the VM builds up enough credits, you can burst your usage up to 100% of the vCPU for the period of time your application requires the higher CPU performance.

The B-series VMs are available in Windows and Linux variants.

There are quite variety of other types of VMs including DC series, designed to protect confidentiality and integrity of code and data.