To answer the OP's question about the Extech 330, I have two of its little brother - Extech 320 (minus the capacitance and temperature function), otherwise same form factor and display.
Both meters are slightly off out of the box, so it gave me a reason to open them up and adjust them using the voltage reference I have. I can tell you the horror story about the 330 build quality is true, soldering was of poor quality, it resembles more of a home-made kit made by someone without much soldering skill. I use these two meters periodically, and neither of them have failed, properly adjusted (there are 2 pots in the 320, 4 pots in the 330), they give reasonable accuracy, not great. I would put these meters in the low-mid end market, if I can only have one meter, they will not be the one I pick.
I do not have the Fluke 115, but I have a new Fluke 179. It does not have the NIST cert option, but out of the box, the meter was spot-on against the reference. If there's any difference, it is in the last digit, well within specification. The build quality is excellent, it is a meter you can trust out in the field. But as other have pointed out, it is more geared towards electrician, and not for bench work if you need high resolution in the low current/voltage range. I think the 87 V might be a better all-purpose meter for mixed use.
For hand held meters, the calibration only involves 1-3 pots in the low end models (typically DC voltage and AC voltage). You can easily accomplish this with a cheap e-Bay voltage standard and an calibrated function generator. For more sophisticated ones like the higher end Fluke, the cal is done through the control and there is no need to open up the case, but there are a lot more test points which would require more cal equipment.
No experience with the Bryman, but if Dave trust them, I trust his judgement.