Do I need to be a member of iOS Developers program to develop and install an app on my iPad ?
Or can I just run Xcode and specify the device on which to install it ?
Without being a member, you can only run your app in the simulator. You must be a paid member to be able to install the app on a device.
You can do it if the iPad is Jailbroken. But that means you have to Jailbreak your device and the app may not work on non jailbroken devices, as you cannot test in the live enviroment.
If you join the dev programme you will get the beta downloads of iOS as well as being able to submit to the app store.
My advice would be, if you want to hang onto your cash for a while longer, develop the app, test it in the simulator that comes from downloading xCode, and once you are happy with it join the program.