The AX720 is your best bang for you buck, period. IMO, everything from there is a marginal increase from the perspective of a non-audiophile. People here (myself included) say things like "it's so much better" or "sounds like crap" and in reality, it's all relative. These are strong descriptors but are describing smaller differences than you might be led to believe.
The A40 + mixamp, although Shin hates the A40s, is a great combo for a lot of reasons. It's a small step up from the AX720 system, but again, not a huge one.
The rest of the solutions would involve buying the mixamp separate, and then buying the headphones you want separate also. This offers you the flexibility to choose from more headphones than the A40 which comes with the A40 system (with mixamp).
I haven't heard the CAL, so I won't comment on its sound. I will say that I'm not a fan of gluing or velcroing microphones on the side of headphones though. I did it on my AD700s with the same labtec mic Shin used on his CALs, and it was great at first, but over time it was just annoying how much I had to baby them so as to be careful with the mic. That particular mic is also mostly rigid and not as flexible as other solutions, which makes it a heck of a lever arm to break itself off. Shin doesn't use a mic as much so it might work for him, but for me, I never game without a mic, so a durable permanent solution is worth it to me.
I wouldn't bother with the AD700s. The complete lack of bass is a deal breaker for me, even though they have great positioning (probably the best I've heard) in terms of identifying where enemies are in FPS games that use sound well (like COD4/MW2). The A40s come really damn close to the AD700s positioning, but have more bass (but not too much at all) and are more rugged and just better all around. At this point, I'll also say that I think the A40s are a great overall headset, well worth $100, but not at all worth the $200 price tag if you buy them separate from the mixamp. When you get them for basically $120 when you buy with the A40 system (since the mixamp which you need no matter what is $130 anyway and the system is $250), I think they are a good deal at this price.
The DT880s are geat for single player gaming but terrible for multiplayer because they their positioning sucks. They are my favorite for music and single player gaming, but they would be among my last choices for multiplayer gaming (since I play mostly FPS games and rely on great positioning).
The K702 are generally touted as the best we can reasonably get for multiplayer gaming. This is for a few reasons. First, they are high quality headphones to begin with, with great clarity and nice smoothness and natural sound, if a little bright. Second, their sound signature works well for multiplayer gaming. They have about as much bass as I think a headphone can get and still offer great positioning (somewhere between the A40 and AD700, but these 3 are all pretty close). Just FYI, the bass is still a little less than you might like, but it seems that bass and positioning tend to go hand in hand, where headphones with great positioning have less bass and vice versa. IMO, it's still enough bass to please, though. The third reason, is because they are easily modified to be a permanent and rugged gaming solution with a mic by using the cable/mic from our very own member SID3W8Z here. His cable attaches to the quick disconnect cable jack on the headphone (K702 only, not found on the K701), and then there is a microphone jack to plug the mic into. You can plug it in when you need it and easily remove it when you don't, very simple, and very rugged and professional (not like gluing or velcroing a mic to other headphones). So there are the pros of the K702, great sound quality, positioning, and gaming flexibility. But there are also some drawbacks to this headphone too. My biggest problem with recommending it, is that it is a hard to drive headphone, which means that you might not get enough volume out of it from the mixamp alone and might require an external amp. I say might, because it is heavily dependent on how much voice chat you mix in with the mixamp. If you find that you need to mix in a lot of voice, you might find that you don't like how much overall volume you then get out of the K702 with the mixamp. If you mix in less voice (or no voice), the mixamp will be more than enough to get them louder than you could want. Some people find that even when they mix in voice, it's loud enough for them, and others (like myself) find that it is not loud enough at all, and need an external amp. Should you go the K702 route and find yourself needing more volume, a good starter amp which has plenty of power to do the job is the bravo v2 which you can get on ebay for around $30-60 shipped depending on winning bid. For me, this headphone is worth it to me for the reasons I mentioned, but I've been squeezing the last drops of quality out of my gaming setup for a while, and I don't mind spending a lot to get relatively small gains (because to me, those gains are worth it).
So, if you want the 80% solution, grab the AX720. If you want the 87% solution, grab the A40 system. If you want the 95% solution, grab the K702 + mixamp + gaming cable (+ maybe external amp, depending on how the volume pans out for your preferences).
I should note that IMO, the A40s and the K702s are not ideal for single player gaming (although you can definitely use them for it!!) due to having a little less bass and being more focused on positioning/detail and multiplayer gaming needs. I haven't heard the AX720 personally, so I can't comment on how its positioning or SP gaming qualities compare, I can only go on the reviews and comparisons I've heard of it. In any case, there really isn't any one headphone which is "the best" at everything - single player gaming, multiplayer gaming, movies, music, etc. You can choose best in one of those categories and average in the others, or above average in a couple and average in others, etc. It's all balance, and no one headphone can do all jobs the best (at this point, based on my experience and opinion). Each of those things require differing sound signatures and qualities from the headphones in order to be the best (IMO), so it's physically not possible. I say pick a headphone that is "the best" or above average at the things you will use it for the most, and just deal with how it performs at the other tasks you won't use it for as much. Or get sucked in and buy multiple pairs of headphones for each task like some of us
Now, for music, that's a whoooleee different ball game. When you get into music, there are so many more viable headphone options, and so many people have so many different opinions on what they like and look for. What I can say, is that if you want to get serious about it, and get the most out of your headphones, you absolutely need a DAC, and the uDAC is a great starter at $99. Without a proper DAC, you are really cheating yourself out of the potential of your headphones. You also should get a dedicated headphone amp, and again, I feel that the bravo v2 is a great deal for it's price. Out of the headphones above, my favorites with music are the DT880 and the K702. The DT880 are well rounded and probably my favorite, and the K702 are a little brighter and awesome on light stuff, but are a little lacking on anything heavier. Really, I think they both have their place. I personally do not like the AD700 or A40s with music, in comparison, even a little tiny bit. There is no comparison to headphones on that level to headphones on the DT880/K702/etc level.