I don't take any special precautions as far as not touching any specific parts of the hardware, at all, aside from the obvious common sense guidance of not trying to pick up or handle parts of things that might be especially brittle, or weak, or liable to break off easily. Other than that, modern motherboards are somewhat protected by special coatings, as are the PCBs on graphics cards etc.
I've built hundreds of systems through the years, and repaired or upgraded hundreds more, literally, and I have only ever seen one system that actually expressed any problems due to static electricity and that was an already built, functional system, where the guy was walking across carpet and holding that static charge and then passing it to the system every time he plugged in or unplugged a USB device. Putting down one of those heavy plastic floor mats meant for office chairs solved that problem.
Other than that, simply discharging yourself on any metal object OTHER than the case (Unless no hardware is yet installed in it) or the hardware itself first is really all you need to do. Also, as I said, don't built your system in area where you are likely to walk across thick carpet wearing socks, or at least be sure to discharge yourself first if you do. Don't wear heavy sweaters made from material that is likely to generate a static charge from you moving around while wearing it. Simple common sense things like that.
If you REALLY feel like you need to get an anti-static mat, how much are you willing to pay for one, because most of the cheap ones won't really do much of anything anyhow.