Billing
According to Windows Azure Virtual Machines Pricing Details, Virtual Machines are charged by the minute (of wall clock time). Prices are listed as hourly rates (60 minutes) and are billed based on total number of minutes when the VMs run for a partial hour.
In July 2013, 1 Small VM (1 virtual core) costs $0.09/hr; 8 Small VMs (8 virtual cores) cost $0.72/hr; 1 Extra Large VM (8 virtual cores) cost $0.72/hr (same as 8 Small VMs).
VM Sizes and Performance
The VMs sizes differ not only in number of cores and RAM, but also on network I/O performance, ranging from 100 Mbps for Small to 800 Mbps for Extra Large.
Extra Small VMs are rather limited in CPU and I/O power and are inadequate for workloads such as you described.
For single-threaded, I/O bound applications such as described in the question, an Extra Large VM could have an edge because of faster response times for each request.
It's also advisable to benchmark workloads running 2, 4 or more processes per core. For instance, 2 or 4 processes in a Small VM and 16, 32 or more processes in an Extra Large VM, to find the adequate balance between CPU and I/O loads (provided you don't use more RAM than is available).
Auto-scaling
Auto-scaling Virtual Machines is built-into Windows Azure directly. It can be based either on CPU load or Windows Azure Queues length.
Another alternative is to use specialized tools or services to monitor load across the servers and run PowerShell scripts to add or remove virtual machines as needed.
Auto-run
You can use the Windows Scheduler to automatically run tasks when Windows starts.