You don't need a wildcard certificate, unless you want to host a lot of subdomains. If you need one just for mysql.yourdomain.com, you can still get a regular certificate, it just won't apply to www.yourdomain.com. Also, you can always get two.

The main difference between GoDaddy's certificates (and similar) and more expensive ones like Thawte and VeriSign is that the former ones are chained. This means browsers don't trust GoDaddy directly. They have to verify their certificate with whatever provider they are using. This is generally not a problem, but does require one extra step from you when setting up the certificate. GoDaddy has instructions.