Create DB2 on networked drive but managing from Windows
As Lennart says, you cannot access the data without the engine. You must install the engine on an OS somewhere. Can this be a central server? Most definitely. That is how the businesses I have worked for have set up there databases, regardless of whether they were DB2 LUW, DB2 for i, or SQL Server.

So you will want to pick the OS your DB2 installs on. IMHO, I'd stay away from Windows. That pushes you to Linux or AIX. My experience was with AIX and Windows. But I have heard good things about DB2 on Linux.

Anyway....you will need to install DB2 on a central server. Data Studio is great for access and/or some management. The DB2 Express-C will be great for you to play around with most things locally before moving them to the server. Keep in mind, not every feature is available on Express-C.