The problem componetns are WiFi and the GPU.
For the GPU, make sure it's an Intel CPU. All Intel CPUs have Intel
integrated graphics controllers, and these are the only ones that work
without proprietary blobs in Linux.
For wireless, you have to get something old, because that's completely
screwed at the moment. Think Penguin and Technoethical sell the only wireless
hardware that works with Linux-libre. Chances are high you'll have to use a
wireless dongle, or just live with Ethernet.
If you want the easiest route for a pretty modern desktop computer, go to
Think Penguin. All their hardware is chosen to work with Linux-libre:
http://libre.thinkpenguin.com
