I would say yes...
We assume you are wanting to run some linux distribution but your question is a little vague. And what do you mean by access your document file? Are you wanting to connect to your desktop? What are you using now for email and banking? I also assume that your banking is accomplished via a web browser. Some bank websites do not like linux web browsers. In most case Firefox should work ok.
Assuming your wanting to install linux check out
http://tuxmobil.org/ and the HCL on this site to see which ones are the most compatable. I might guess that built in wireless would be somewhat important. Wireless chipsets vary between manufactures so this might be important for "out of the box" support. Graphics adapters might also be high on the list but not really important for basic email and web browsing. These days the min RAM is 1GB.
Some laptops have built in card readers which can be somewhat difficult to get working or may not be supported in linux at all.
Basically most any laptop would fit your requirements so it really comes down to price and ergonomics i.e. how well does it fit your person.
