It is quite safe.
Easy? That depends on who is driving the computer. The documented procedures are not easy for computer neophytes, especially for the ones that can not figure out how to troubleshoot driver installation problems, or are unfamiliar with using the command prompt.
I don't know if your phone can be rooted, because all you said is "updated it yesterday". That means very little frankly, because there are ways of doing that that will prevent root, and ways that do not. If by "updated" you mean the OTA (Over The Air) 2.1 update, then your phone probably can be rooted. The thing that determines whether or not you can be rooted is not the OS version, it is the bootloader. You want to see "1.46 S-ON" or "1.47 S-ON" at the top of the display (power your phone on by holding both the Send+End/Power button at the same time to see this). If you see "S-ON" in the first line, and 1.49.0000 in the second line, you can not root.
You can follow the guide (Sticky) at the top of this forum. It is the same procedure for rooting a "1.5" phone or "2.1" phone, so long as they have a 1.46 or 1.47 bootloader. The one piece of advice that I will give you is that you should get the SDK and HTC driver for ADB working correctly before you root your phone. After you have done that, everything else will be a breeze.
eu1