I agree with much of the above, but I would say "it depends".
It depends on what trails you intend to do. If you intend to stick to easy to moderate trails, no problem. Everybody should move along at a good pace. However if you intend to do the more hardcore trails, there are pluses and minuses to going during EJS.
On the plus side, you can be assured of plenty of help should you be the one broken down or in need of help. But if you go during any spring week, from about April 1st to June 1st, the trails will have people on them. They won't be crowded, but they won't be empty either. If you get into a bind, someone will come along sooner or later. In the fall, its not uncommon to be the only person / group on the trail.
On the minus side, people do break down and usually on the harder obstacles. If there is no bypass, you can be stuck for an hour or two while the rig is fixed or moved aside. I know from personal experience. Even if no one breaks down, some of the harder trails can take all day and well into the night to complete. Poison Spider / Golden Spike / Gold Bar Rim is a classic example. Very popular trail. And if you are at inclined for a challenging trail, its hard to beat. A fair amount of bypasses, but not everywhere (the wall on GBR is a good example). The trail is challenging but provides exactly what most people on 35s or 37s come to Moab for - let it hang out a bit. Get on the edge. Just be prepared if you do it with the EJS group or behind the EJS group, you will most likely not be back to your hotel / condo / campground until well after dark. If that doesn't bother you, go for it. If that is a concern, well then consider other options.
As pointed out above it also depends on your tolerance for delays and long days on the trail. Some people think that is what it is all about. Other people get pretty damn cranky if they miss their supper at the favorite restaurant.
I guess my advice to a first timer would be to come after EJS is over. The week immediately after EJS is often still pretty busy with lots of jeeps. But don't forget, there is Hummer Week, and Toyota Week (not what they call it but you get the idea), Jeep Jamboree, and so on. EJS is the premier event, but you can go during a similar event and not have quite the crowds, but still plenty of people.
As far as getting lost on the trails, Funtreks sells a data card that fits in some GPS models. It has all of the popular trails in Moab on it and make trail finding and following foolproof. Its the best $40 I ever spent.
And don't be too concerned about my talk of breakdowns and such. Yes, they can happen. But if you are prudent with the skinny pedal, know when to lock and unlock, and pick decent lines, breakdowns are rare. I go twice a year with a large group and we have only had minor breakdowns.