Terry,
A lot of the posters here have gotten it dead on. Every ARTCC is perfect for some people and not so great for others. I know many people at ZLA would find the traffic levels at some of the slower ARTCCs less stimulating, while others prefer the slower pace and less difficulty.
There are a few things you can look at though to get some idea of what you are getting yourself into, that in my experience matter very much. Here are the kind of questions you should ask:
1) Does the ARTCC staff their positions? Although there's something to be said for going to a less-staffed ARTCC in an attempt to build them up, advancing at a dead ARTCC can be difficult if nobody is staffing positions and there aren't many instructional resources available. It is also harder to draw traffic for your sessions if the Center position is not staffed on a regular basis.
2) What is the training department like at the ARTCC? Every training department is different. Write the Training Administrator or Air Traffic Manager of the ARTCCs you are interested and ask them for their thoughts, look at the publicly available materials on their websites, observe a little bit at the ARTCC, and ask students going through the program for their opinions.
3) Do the ARTCC Staff members exist and stay active? An issue that can crop up at an ARTCC is the staff not being online. Look at whether the ARTCC Staff instructs, controls on at least a semi-regular basis, and in general shows a presence in the ARTCC. Advancement becomes very difficult if the training and administrative staffs aren't active. Do they reply to your e-mails promptly?
4) How are the ARTCCs forums and/or Teamspeak server? This seems like a minor point, but it's one worth considering. Do you like the attitude of the members in the forums? Do the people seem like the kind of people you want to control with? Does the staff seem knowledgeable, friendly, and mature? Does the place seem dead?
5) What do you want in an ARTCC? The learning curve at ARTCCs differs drastically depending on the traffic and complexity of the airspace, and the philosophy of the training department. Some ARTCCs demand substantial off the scope effort as well live training, while others do not. Some people like having a geographic connection to the airspace, as it can help them learn it more easily, others don't care. I find working lots of planes every night and constantly being challenged really fun. That's why I keep coming back. I know plenty of people completely satisfied at other places for their reasons.
That's really just the beginning of the list. Making a good choice can be the difference between enjoying this hobby and not.
Finally, remember that if you don't make the right choice, you can always visit elsewhere, or transfer. People transfer for all sorts of reasons. I transferred twice because I had reached the top at previous ARTCCs, only to discover that there was a bigger challenge worth attempting. If you make the wrong choice, you may find another place is better for you.
Hope that helps!