Something very important that has not been mentioned yet that your usage pattern will be unsuitable for NiMh batteries (ie regular AA rechargeables). Normal (non-low self discharge) NiMh should really charged every month because they discharge themselves so quickly. If you were to buy low self discharge NiMh it would push your price over your price bracket. I am not an expert on batteries by any means but if you were to leave your light unused for long periods of time while you were away, it would be detrimental to the batteries and you would come back to a light with dead batteries.
I would also second the ultrafire WF-500 or WF-600 to you in this situation. If I recall correctly, the WF-500 is a hotwire; the WF-600 is LED. You will also need 2 rechargeable lithium ion batteries and a charger. Lithium ions don't have the same high self discharge problem that NiMh does. Please make sure that you read up about the dangers of lithium ion batteries (see the sticky thread in flashlight batteries and electronics) before you embark down that route though. Where it comes to lithium batteries, cheapest is not best and is certainly not safest.
The WF-600 is available cheaply from
http://www.dealextreme.com/details.dx/sku.9428
The WF-500 is here:
http://www.dealextreme.com/details.dx/sku.1317
And replacement bulbs for the WF-500 are here:
http://www.dealextreme.com/details.dx/sku.3144
For sheer bang for buck, the cheapest thrills are found from 20 or more million candlepower lanterns. They are large and usually use lead acid batteries but should quite easily fall within your price range. This option will almost certainly give you the brightest light for the least money.
Something like
this (but for less than your $40 budget) should be available from your local hardware stores.
I hope this helps you.