GUEST,Novice - As you have a Windsor, I am assuming you are UK based?

I've had good sets of strings from various brands.
D'Addario, Ernie Ball, La Bella, Vega strings (now seem to be Martin/Vega), The Music Room at Cleckheaton sell Redwing, which are good quality and inexpensive. Eagle Music at Huddersfield also offer their "own brand", which I haven't tried, but would expect to be decent quality.
Only you can decide if you prefer light, medium or heavy gauge strings. They can give a different feel and tone to a particular instrument.

As for the vellum. you need a heavy thicker vellum specifically for banjo (Eagle Music will sell you one). A drum skin may be thinner and not take the pressure of strings pushing the bridge down. If you need advice on actually fitting the vellum, ask here. The subject has been discussed previously, and it should be possible to find the discussion without having to repeat it all here.

Quack!
Geoff the Duck.