wyantm06,
You really don't need the grounding strap, but if it makes you more comfortable it won't hurt. I just built my most recent machine a couple weeks ago, acrylic case on carpet, nothing fried, just had a power supply plugged in next to me so I could discharge static when I felt like it. Handle all parts by thier edges or frames in the case of drives. And make sure that what you are discharging/grounding to is bare metal and plugged in.
Glaive