As I understand it, the arthropod's six legs are such because they are more efficient. Six legs means keeping three down - your basic three-legged stool - while moving the other three forward to become your next base. Easy-peasy, doesn't take much in the way of brains to control it - and there ain't much brain to an insect, so it works for them. Less is awkward (watch how a mantis has to move in order to free those forelegs for its infamous grab). More is doable but means added investment in body - without an obvious reward, the six-legger has an advantage.
Arachnids have that obvious reward. They follow a different path: 8 legs. Workable - four-legged chair - and it left them in a good position to switch to the six-legged gait and evolve two legs into other uses. For the six-leggers on the other hand, freeing up the forelegs involved coming up with a new way to get around (ex.: grasshoppers).
And then there are the wings: insects have six legs, but they frequently manage to evolve a bit of that carapace into a rather effective flying appendage. Doesn't scale up well, but very effective on their scale.
Then there are the many-legs. Simple architecture, simple gait - a ripple of many legs on either side of a long narrow body. They've held onto their ecological niche for that reason, but there isn't a lot of potential for improvement and it doesn't scale up well, so they're never going to get much bigger than they already are - although there are some rather impressively big examples of them.
When fish crawled up onto land and started their evolutionary bit, a new gait was established: tetrapod. This is a "falling" gait: keep two legs under you and shove forward with them while swinging the other two around to catch you, then repeat. Time and circumstance saw that evolve into some marvelously effective tetrapodal gaits - and some of novel departures (Us and kangaroos, for example).
When contemplating your new species, first think of it in terms of mechanics: How do they get around? How do they move from point A to point B? Two legs? Four legs? Six legs? More? Most likely their legs are under them - that seems to be the most energy-efficient way for larger species.
Next, ask how they managed to evolve a set of manipulative appendages? Humans evolved from four leggers who learned to climb trees and then came back down. Others with roughly similar appendages - not necessarily acquired in quite the same way - include rats, mice, chipmunks and racoons. There are many examples of dinosaurs who depend on a tail to maintain a see-saw kind of balance that frees up their forelegs for other needs - some of whom evolved those forelimbs into dandy wings. And, the kangaroo found it more effective to bound on two legs than to run on four - though to be honest they really didn't take full advantage of the opportunities that presented for their forelimbs.
A six-legger is not inconceivable - if the first lobe-finned fish had had a couple more lobes, we could look more like centaurs than like apes with exceptional balance. Eight legs offers clear possibilities: you can free up four limbs by adopting a four-legged gait, leaving you with the possibility of a centaur-form with four arms, or a form with forearms and a set of arms "amidships", or a form with arms both fore and aft.
Consider Mike's observation and make the carapace vestigial. Evolution gave them an inner skeleton to help support weight and allow larger growth, and evolution of larger forms favored the inner skeleton: the outer carapace became a carapace-and-hide affair for increased flexibility and growth, then the carapace grew smaller and smaller as species grew larger and larger until the various species evolved to that form have hides that are more like rhino hide with small vestigial studs of carapace scattered on them.
Now here's a wierd form: 8-limbed, four legs with pairs of arms forward and aft, a head squarely in the center of the "back", excretory orifices on the "belly" centered between the four legs. The head turns through more than 180 degrees, so an outside observer may not be able to tell which end is the front and which is the back - if the body is squarish, he may not be able to tell the sides from the front either. Consider multiple eyes offering 360 degree vision. Now you have a sapient with a truly strange philosophical view, from the human point of view: where we tend to view life in terms of going forward and backward, they tend to view life as a plane with many equally acceptable directions.
Or, you could eschew limbs altogether and just design something like a telekinetic intelligent clam.
(Until then, I want to keep them a surprise.)