You've got a bunch of questions going on here, but I'll see if I can break this down in a reasonable manner.
For starters, there's another key part of your phone that can be useful for determining which rooting methods will/won't work - your HBoot version. This is effectively a first-stage bootloader for your phone, and you can access it by powering on your EVO while holding the volume down button. You'll know you're at the HBoot screen if you get a mostly white screen with some skateboarding androids on the bottom. It will look something like this, and will have text that says "HBOOT-
<some numbers>" near the top. This is your HBoot version, and it's good to remember what it is.
Second, that rooting method is, as noted, outdated. I believe people currently use this method or this method on the 3.70 software. You could also try Unrevoked if you want, but I don't know how nicely it plays with 3.70 (especially if you have an HBoot version of 2.02 or later). I have not had to root in a while, though, so I'd just look through some threads a bit to see what is working on your software versions.
You do need root in order to flash a custom ROM image on your phone. Pretty much every rooting process now will unlock the permissions of your NAND, which is the portion of flash memory where system files live. You need to be able to write to NAND in order to flash a custom ROM, and you need root to perform the unlock.
The easiest way to flash a ROM is through a custom recovery image. You can put a flashable .zip file on your SD card, then boot into recovery and flash the .zip to install the ROM. The ROM itself will pretty much always be rooted, unless it's just an unmodified OTA that's been packed into a .zip format. You can also flash ROMs directly from the ROM Manager program, but it can be a little finicky, so I recommend doing it manually. The two main custom recoveries are Amon RA's recovery and ClockworkMod recovery (brief discussion on the differences here on XDA).
Custom recoveries can do other things, too, such as partition your SD card and perform NAND backups. If you're going to start rooting, I recommend making a NAND (also called "nandroid") backup any time you are getting ready to make a modification to your system. The backup is a literal 1-to-1 image copy of your NAND when the backup is made, so you can completely restore your phone's current condition (settings, system, apps, everything) by restoring from a backup.
Lastly, it is possible to unroot your phone. If something gets really messed up, you can use one of HTC's ROM Upgrade Utilities (RUU) to effectively re-flash the phone back to stock HTC software. When mucking around with dual-booting ROMs on my EVO I managed to wreck my boot partition at one point. I couldn't get into my ROM, I couldn't get into recovery, but I could still get to HBoot. From HBoot I could still run an RUU, so I just restored to the 3.30 software, re-rooted, restored my NAND backup and went on my merry way. Although there is always potential to brick your phone completely, I've never actually seen a scenario where a phone couldn't be recovered via HBoot somehow (either RUU or another method). There are guides available for this as well.
Also, just as a note, if you only want to root so that you can get rid of Sprint's bloatware, you don't need a custom ROM. Once you unlock your NAND you can just delete apps from the /system/apps directory via an
adb shell or a terminal emulator. I personally think it's worth it to dive into a custom ROM (I'm a CyanogenMod guy myself), but that's up to you.
And of course, if Sprint finds out that you rooted your phone your warranty is void. I think it's worth the risk, but it's something to always keep in mind.