Not quite sure how far you want to take this.
If all you want to do is have access to files on your desktop, all you will need is a null modem cable, and use direct cable connect.
If you want a permanent connection, without having to plug/unplug the null modem, then you might want to move to wireless. The bare minimum you will need is a standard NIC card for your PC, a small 4 port hub, a wireless access point, and a wireless NIC for your laptop.
There is no way around the Access point, as wireless will not emulate crossover connections to the best of my knowledge. I may be wrong, but technology changes daily.
actually, there is, if you connect the access point to your Desktop with a crossover cable, but a cheap 4port hub is less than $40.00, and becomes important later.
The whole package I described above could be had for around $600.00, maybe less. Prices change daily too.
The beauty of this setup is that your pc and laptop are always connected. The access point and hub are setup where your desktop is, since the desktop doesn't move.
If and when you decide to go ADSL or Cable Modem, the 4 port hub will also provide your connection.
Pros - again, as with caller 1, freedom to roam with your laptop, especially if you go the internet route.
Cons - depends on the size of your home. The low end wireless access points are limited to about 10 meters. Ranges improve as price rises.
Wireless right now is limited to 11 mps, but as its just you and trusty old desktop, that's not a real limitation.