@Eddy Uk' Thank you for your question and interest in Azure.
For clarity, I am not allowed to issue a price quote. I can however make some suggestions, which you can then input into the Azure Pricing calculator. This will then give you a rough estimate.
Starting off, this sounds like a less demanding site. I would make two recommendations for the Azure App Service pricing tier. You could in theory try a basic tier, such as a B1 instance. The basic tier provides you with 10 GB of disk space, which I assume is enough for your site content and DB. Or you could consider jumping up to the standard tier with something like an S1 instance. The standard tier is technically what we recommend as a minimum for production work loads. The standard tier does cost slightly more and offers additional features that go far beyond what you've listed out. Either way, take a look at the Azure App Service pricing page (link) to see all the features available with each tier. (Be sure to select the correct OS, data center region, and currency as these variables impact the pricing)
Regarding your database, this sounds like a rather simple and straight forward DB. Have you considered running your database directly on the App Service? This can be achieved with something such as MySQL. The pro is this helps to remove any DB cost, since you're running it on the web app you're already paying for. The downside to this is it will use the same resources as your web app. If your DB grows, you might need to look into moving the MySQL DB off the App Service and into a dedicated MySQL instance. More information on App Service + MySQL can be found here.
Azure Web Apps supports you using a 3rd party domain provider, or we also provide domain purchasing services. If you already own a custom domain via a 3rd party, please see these steps here, which show you how to link your custom domain to your web app. If you would like to purchase a custom domain through Azure, please see these steps here on how to do so. For pricing information on Azure custom domains, please navigate to here and scroll down to the "App Service Domain" section. (Again, be sure to select the correct OS, data center region, and currency as these parameters all impact pricing.)
For SSL, we support you using a 3rd party SSL certificate provider or we also provide the ability to acquire SSL certificates via Azure. If you have a certificate from a 3rd party provider, please see these steps here on how to upload it. If you would like to acquire an SSL certificate via Azure, we have two options. Azure App Service Managed certificates are a free option. More information can be found on it here. We also offer standard and wild-card SSL certificates. Pricing information on those can be found by navigating here, and navigating to the "Azure App Service Certificates" section.
I hope this helps provide you with some concrete information. Most of the links include pricing, as long as you input the correct parameters. Please also check out the pricing calculator, which can be found here.
Lastly, if you're looking for a formal price quote to provide a client, you will need an Azure subscription, which will then allow you to create support cases. If you have an Azure subscription, you can create a free billing ticket here to receive an exact price quote as those employees are empowered to give exact pricing guidance.
Please let me know if you have any further questions or concerns and I would be happy to answer them.