I am new to linux. I want to construct a new computer that will operate linux. Should I only choose hardware (like a TV tuner card or a sound card) for which there are already linux drivers or are there always workarounds for getting every piece of hardware working on linux even if there are no drivers? Are these workarounds easy to implement or will I spend a lot of time and effort trying to get the hardware to work?

The workarounds are just that-- workarounds. They may get the hardware working completely, partially, or barely. I would suggest you do a build up based on hardware that is known to work with linux then give us a post here with your specs and ask for opinions or probable pitfalls.

If you can find hardware that does what you want and it has linux support for it. That's the way to go. When you find something you want to buy just search here or do a google search for the model + linux and see if you see any good "how to's" or pitfalls with getting it to work in linux. Also be sure to search for the specific linux distro you are using as support could change from distro to distro. Most popular pieces of hardware will have "some" linux support, some will be easier to configure than others. But it's best to do your homework first or be prepared to go to the ends of the earth to get it working.

Welcome to LQ.
Yes, however, from my own experience, the linux drivers provided by a manufacturer are not as good as you'd expect.
Before you buy any hardware like tv-tuner, etc. it's always best to google for a particular model and check if people have successfully used it with linux.
There's also a Hardware Compatibility List section of LinuxQuestions where you can find some reviews of various hardware.
http://www.linuxquestions.org/hcl/
have fun

The suggestion of looking at the HCL is excellent. Also search LQ and see if a lot of people are having problems with a particular device and check out the distribution of your choice for support and issues also if you want a 'smooth ride', if you don't mind bumps and beating your head on the wall potentially, just grab what you like you'll probably be fine there is SOME support for almost everything, but be prepared to wait and fight with the components.