setting up a wireless network

[Martin Ericsson]

Hi!
I have a desktop computer but will get a new laptop soon, so I want to 
set up a local wireless network. My desktop makes a lot of noise, so I 
figure I'll buy a router. But I don't really know what you can do with a 
router.

This is what I want:
1. share the one static IP I get from my internet provider so I can 
access internet from both computers.

2. being able to access (at least) my desktop computer from the internet 
so I can use it as a ssh/webb/whatever-server.

3. share a folder on my desktop computer with the laptop (via nfs?)

4. connect between the computers via ssh. I want the (local) 
IP-addresses to be constant so I don't have to find out what the current 
IP-addres for e.g. laptop is if i want to access it from the desktop.

Can I achieve this with a standard linksys wireless router?

Martin Ericsson