What you are looking for is
XAMPP Portable Lite
XAMPP is a "Apache distribution containing MySQL, PHP and Perl" and you can use it for developing your website on your local pc.
You need to create an A record for sqldb1234.db in your DNS area for GoDaddy.
Once the A record has propagated you should be able to use the subdomain sqldb1234.db.mydomain.com in your connection string.
If you're talking about dedicated servers, then it won't be such a big problem to transfer the database.
You can use SSH in order to transfer it directly from one server to another, without even downloading it. Then you can import it in a new database from the command line pretty fast.
If you don't want to worry about storage and performances, then go for ...
Since you mentioned you might be open to considering an entire new solution to the problem, my preferred approach here would be instead of connecting via ODBC from your linux server to the SQL server,
Setup Apache/IIS and PHP on the SQL server,
Create an API written in PHP to perform the database queries required via ODBC but executed directly on the SQL ...
What you need is any kind of a so-called "WAMP stack". There are many solutions out there to choose from, see a comparison of WAMPs.
Although the most popular one is probably XAMPP, my recommendation would be to use Uniform Server instead. Uniform Server is much lighter and easier to manage than XAMPP. And it doesn't need an installation, so you can even ...
It's pretty standard practice to have a data warehouse separate from your application database to run reports off of. This keeps your app from slowing down when generating reports and allows you to keep more data and in a more suitable (denormalized if necessary) format for running reports.
It's analogous in principle to Command Query Separation/CQRS in ...
Not sure how GoDaddy has their servers set up, but many/most web hosts run dedicated MySQL servers, offloading the DB workload from the web server. As for security, SQL Server 2008 at least supports cell-level encryption like Server 2005 as well as full database-level encryption. Windows also supports file-level encryption via EFS and BitLocker. Given these ...