I would use WCF because it can do everything webservices (asmx) does; while giving you the flexibility to extend much further.
You can setup a simple WCF Service just as easily as an ASMX service through Visual Studio. So if you're "Fresh" on both technologies, I'd spend time learning WCF.
Depending on your specific use-case, you might might also look into WCF Data Services (.NET4) and Entity Framework. It basically gives you a nice API that you can use to consume your database over http/https. The beauty of WCF Data Services, is that you end up writing very little code to get at your data, and you can focus on consuming it.
WCF Getting Started -- http://msdn.microsoft.com/en-us/library/ms734712.aspx
WCF Data Services -- http://msdn.microsoft.com/en-us/data/ee720180.aspx