What most people use for audax is the Hope Vision 1 which is about £70. Having two is ideal. You'd need to carry spare batteries on LEL. The other excellent but affordable option is the B&M Ixon IQ.
@PPete:
It may be that the combination of your riding style and setup means you never suffer from the problem, but there is no doubt that triples do unship more than doubles. Triples are simply more complex and require more compromises to cope with the greater variety of shifts. In particular, the small chainring is a long way from the front mech and shifting down to it is when most problems occur.
If you need convincing, have a look at the excellent thread on the CTC forum started by MickF. As Mick says, when you get to know a triple you learn exactly what kind of shift is likely to make the chain come off. Mick attached a video camera to his seat tube and filmed it - the amount of flex in the system is amazing!
For me it was generally when I wanted to go from descending in a high gear to climbing in a low one while keeping power on to carry me up the hill - not an uncommon scenario. However, if I backed off the power there would be no problem. It comes down to riding style.
Regarding frames, it really doesn't make much difference what you have, as long as you can get a decent fit on it. A cheap, second hand aluminium frame bike that is set up properly for you will be fine (I have one that is) but you could spend thousands on something that would have you in pain before you got far on it! Money spent on a fitting could save you lots on the bike.