Off the peg I make Mickle right and there's no way you're going to get what you want and match cheap/light/low maintenance. Even if you removed the budget restraint I can't see you getting a bike that weighed much under 30lbs. For example:-
for £3-4k you could put together a rohloff/dynamo combo on a lightweight frame but you'd struggle to get the bare bones in at much under 26lbs. Then you'd need to add another 5lbs for chaincase, mudguards, rack etc. The best you could do, and still spend a fortune, would be with a 3 speed hub gear but that then limits you for useage.
If price is the biggie then I'd look out for a secondhand frame with horizontal dropouts that could accommodate a hub gear wheel of your choice. But even then all the bits are going to mount up unless you're really lucky.
Personally I'd bite the bullet, spend a bit more and aim for something with a bit more versatility. Step outside your opening spec a bit and buy something off the peg that could be modified as parts wear out to match your needs. Maybe look for a cheap 26"/29er with the frame fittings you need and adjustable dropouts. I know
Halfords had some good deals on Voodoo bikes as I nearly got one for one of my sons. If you get the adjustable dropouts then you can always fit a hub gear at a future point with minimal faff. Plus you have a bike that can be used for multiple purposes and maybe worth spending a few quid on some rigid forks as well.
