Hey there!
First off, welcome to the site, glad you're liking it
I want to suggest you go read this:
Rooting - is it for me? Some Q&A | Android Central first. Things change and new phones come out, but this pretty much covers the basics.
Another thing I think you should consider -- do you really need to root your phone? Some of us here (including me!) will root anything that holds still long enough, even if it works just fine and nothing needs changed. Don't listen to that nonsense. You decide if you want to try to improve anything, if your happy with what you have, or if you want to risk your warranty.
Now all the responsible adult kind of talk is done
I have a Mesmerize here that I'm reviewing for the site.
I rooted it, for two reasons:
1. Cause I'm an idiot like that (See second paragraph)
2. Because someone had to see what methods work, and what methods don't.
The Mesmerize is one hell of a phone. US Cellular has one of the best Android phones to date in their line-up now. But it is US Cellular, which means it's never going to be a super popular phone, and the third party development community (the hackers) is going to be very small. There won't be hundred page long forum posts about rooting, or customizing the ROM. There will be some, I'm sure some hackers are using US Cellular for their carrier.
If you decide to root the phone,
DON'T FOLLOW INSTRUCTIONS FOR ANY OTHER PHONE, NO MATTER HOW SIMILAR THEY APPEAR TO BE. The Mesmerize is not the Fascinate, or the Vibrant, and will need/use it's own techniques for removing some stock apps, or tweaking the system. I'm sure that somewhere a Mesmerize hacker will turn up and all the options you see for phones like the Fascinate will be made available for the Mesmerize. Until then, stick with things that are easy to revert. Root required apps from the Market (Root Explorer, Titanium Backup, etc) are fine, I'm using them myself on the Mesmerize.
Here's what I would suggest --
Go ahead and root your phone. Use the automatic method I mention
HERE. Then stop. Read everything you see about Mesmerize hacking, both here at Android Central and at any other Android site you can find. Don't do anything you don't understand fully, and that a number of people have reported as working well. If you come across an app or hack that says it is for any phone, but needs root, that's you. Read up on it, be sure you understand how to do it (and more importantly, how to undo it) then try it. Ask for help if you're unsure. There are a lot of jerks out there, but there are just as many people who are happy to help someone willing to learn.
Sorry 'bout the wall o' text
Hope this helps, and feel free to ask away if you have questions!