We've used ArcPad for years, but have recently switched to Collector. GPS units that connect to Apple devices need an extra registration with Apple (and not free). However most GPS devices have this feature due to the market reach of Apple.
We use the iSXBlue II with our iPad and it works great. We also use the inexpensive Garmin GLO since it is still better than on-board GPS in iPad. If you want higher accuracy, the SXBlue III would be great - however it doesn't have the apple protocol (the missing "i" in the name actually denotes this). Crazy how they markup the Apple protocol so much in price at Geneq - while the entire GLO works with Apple and doesn't even cost as much as the markup difference - sorry for the vent. However, you still have options...
Some of the same engineers who worked at Geneq (maker of SXBlue), created their own company called EOS. They sell very similar devices (almost too similar), and they all have the Apple protocol on all devices (called Arrow): Comparison Charts – Eos Positioning Systems
A few other devices to check out are from Bad Elf although not sure if they get to the level of accuracy you are working with (Bluetooth GPS - Bad Elf ).
And finally, here is a breakdown of some devices and accuracy when using an iPad with GPS:
ArcGIS Collector External GPS Options - Spatial Times
Hope this can help.