First, you are working with a system (Sarge) that is out-of-date. I would recommend loading Etch with a lightweight desktop like XFCE due to the TP600's limited resources. If I am not wrong, the TP600 (I used to have a 600e) has a max of 256MB RAM. It would not hurt to upgrade it. The main reason that I suggest Etch over Sarge is updated hardware support.
From your post, it looks like you are inquiring about both wired and wireless cards. I was using a 3Com 3C589D wired Ethernet card on my 600e, and it worked well under Linux.
For wireless, I've had my best luck under Linux with WiFi cards that use the Atheros chipset and Atheros Linux driver.
Here are a few links to Linux hardware compatibility sites
that might be of help.
I hope you find these useful. Currently, I am posting this from Ubuntu v.8.04 (Hardy Heron) on a Compaq Evo N600c using a generic "Ativa" 802.11g WiFi card that I picked up at my local Office Depot. I've previously used these cards (I have three) with success on my old IBM TP A21e under Etch, a Compaq Armada M700 running Etch, and on a Toshiba Satellite 2410 Series running both PCLOS "TinyMe" and Puppy Linux 4.1 Retro (22.214.171.124
--- On Tue, 10/28/08, Bernard <firstname.lastname@example.org> wrote:
From: Bernard <email@example.com>
Subject: wireless on an old Thinkpad 600
Date: Tuesday, October 28, 2008, 6:44 PM
Hi to everyone !
I would like to install wireless facilities on my old Thinkpad. It has a
300 Mhz processor, 128 MB of RAM, and 4.1 GB of space on hard disk. It
used to run on RedHat 7.2, which stayed there for about six years without
any problem. Since I have been unable to get wireless working on it using
pcmcia IBM 'EtherJet' card and a router in client mode
'FON2200' (the so
called Fonera), I installed Debian Sarge instead of RedHat 7.