I am not too economically blessed either, so you're not alone.
Luckily I have had the opportunity to buy used laptops from my former employers so I have had second hand laptops for years, and they usually work well. The fine thing about Linux on older hardware is that pretty much everything is supported, even if you may have to Google some and read up on Linux on Laptops
in order to get everything working.
My former laptop was a Dell Latitude CPi A300XT (300MHz, 128MB RAM, 6GB HD, neomagic video chip) which worked exceptionally well untill I dropped it on the ground for the second time.
My current laptop is an IBM Thinkpad 600E, a 366MHz model with 192MB RAM and it works very well. I have upgraded the HD to 40GB and in an instant it became quite a quiet and responsive machine.
The network card I use now is a D-Link DFE-670TXD. It is a 16bit (not 32bit/cardbus) card which is very well supported on all distributions since it uses the standard pcnet_cs driver in the Linux kernel. It is a 10/100mbit autosensing card but since it is a 16bit card it doesn't provide full 100mbit throughput, more like 10mbit. But it is affordable, reliable and works well.
I hope that gets you started.