Hi there,
The sizing will depend completely on what you application is consuming in terms of CPU power, Memory usage and throughput needed. Same goes for the database. There are many options and it is indeed quite difficult to know what to choose upfront.
The best approach in my experience is to pick f.e. a Basic tier deployment (App Service Hosting plan with a B1 VM hosting your site) and find out if the reponse times are adequate for what you need. For the database you could start with a Standard level
(S0) and test where the bottleneck (in case there is one) is located, that could be the DB througput or your website performance.
It is quite simple to scale up from there and eventual outscaling to multiple web server VM's for you site is very simple in Azure (scripting, autoscaling, manually in the portal).
Using the standard build in monitoring features you can quite easily measure your site's response time and compare the results after you switched to a different set of resources.
I have seen many project where a B1 Hosting plan and S0 database were enough, but I would count on that without testing.
Can I assume you already took a look at the Azure pricing calculator?
http://azure.microsoft.com/en-us/pricing/calculator/?scenario=data-management
In terms of costs your Compute hours probably are the biggest part of your monthly billing followed by the DB and then storage (blobs etc.,bandwidth and at the bottom and your transactions on storage). But again that is just based on my experiences
with smaller sized web site audiences.
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