What lens can I get for my camera?

The commonest lens is the 18-55mm AF-S zoom. If you're going used, look for a decent camera dealer who'll offer you a warranty, but just about anywhere that sells cameras, real or online could get a new one for you.

That camera often came with the 18-55 without VR. These days the version with VR is hardly more expensive and it's nice to have. Another good option is nikon's 18-105. If you're not scared of buying used then see if you can get the 18-135. A very underestimated lens that sometimes goes ridiculously cheap.

Your D40x will work with any Nikon AF-S, Sigma HSM or Tamron built-in-motor lens.

Don't bother with a standard lens: Better value to get a Nikon 55-200, F4 to 5.6. You should find a very good used one for £100.

Or to go wider angle, consider a Nikkor 18-55, F3.5 to 5.6. A new one is about £100. A good used one about £70.

If you get both, you'll have all bases covered.