To start off, the desire and nexus one are practically the same phone in hardware sense(!)
The only difference will be the interface of the desire, tweaked by HTC (called "Sense")
While the nexus one will be the stock android hardware, receiving most android updates quicker then the rest (Over The Air from Google, while others have to pass through the manufacturer's).
Don't go for the Wildfire, it seems the most budget friendly but the performance is not to be compared. The processor in it is ancient and you won't be able to run most apps smoothly anymore.
I can guarantee however that the nexus one will be good for those things for at least 2 years (don't know whatsapp tho). I've had it for 1,5 yr now and it's still good. Never kept in a case (just the nice pouch it came with), dropped a good five times (one high drop on concrete) and not a mark on the screen (well the last impact hit the side of it slightly), the metal casing absorbs most of the impact (by denting that is ofc). If you'd drop your phone on the corner of your screen it would normally be game over, but this one is built in such a way that that's practically impossible.
Came with everything needed to read Word Excel PDF etc. Gmail is built in, hotmail can be configured (although I recently just forwarded all my hotmails to my gmail and labeled it "Hotmail", MUCH easier)
For around 250 you'll still have one hell of a smartphone on your hands, you'll find it simplifying things you never thought of (this was my first smartphone too).
It won't be the latest dual-processing, 3D capturing, full HD rendering smartphone but it'll still blow most of the phones in it's priceclass out of the water