You have 3 parameters to look at here. And to say it first, counts do not necessarily reflect precision of a DMM.
The parameters are:
- build quality and the trust that this device will be still within spec after 10 or 20 years
- basic accuracy
- resolution (=counts displayed)
For the sake of longliving, there are only a handful of manufacturers with a proven track of quality build, where one has a significant number of devices availabe after 20 years.
Fluke is the prime suspect here. Nearly every other brand in the market is whether too young with its current lineup of meters, or the stuff is known as not ultimately longliving...
Keysight essentially bought a company to do handhelds, and seems to retract from that market.
Gossen Metrawatt has a quite fresh overhauled lineup of handhelds, which are nicely build, but the older devices (20+ years) were a company they bought and some models had quite some reputation to go stray with old age.
Brymen: I have heard mixed stuff, here in the forum some cal tech mentioned also something about longterm stability of Brymen DMMs he has seen that came in for check.
Acccuracy: In the specs of the DMM is a table with the accuracy related to each value that can be measured. The question here is: What do you work at, and how precise a DMM has to be?
For electric work and repair stuff, 0.5% basic accuracy in DC and 1.5% in AC is quite sufficient- I myself work on battery charging circuits and decided that I need to be able to have Millivolt precision below 10V, so 0.1% DCV accuracy was asked for.
Resolution: Here are the counts of your DMM. Basically the measured value is broken into the number of counts for display.
Lets say, you have a 6000-count DMM that has a 6V and 60V range, and you measure something with 12V, like a car battery.
This DMM has to use the 60V range, and can measure with a resolution of +/- 10mV display accuracy. (On top of the 0.x% accuracy of the DMM itself)
A 20.000 count DMM usually has a 20V range, and can divide in this range to +/- 1mV
Usually multimeters with higher counts are more expensive and have better basic accuracy due to usage of better parts, but this is not guaranteed- so a look at the specs always is mandated.
You can get some high-quality 6000 count multimeter like Fluke 179 oder 87 with a basic acccuracy of 0.09 or 0.05%, and some 10.000 counts multimeter wit 0.1% or worse basic accuracy.
My approach here would be to define which overall accuracy you really need (at which stuff do you work?) and then define the minimum requirements of the device.
For me, doing some repair work and troubleshooting when repairing broken stuff, a 6000 count DMM would be enough to find the faults. For more precision work, like working on battery chargers etc., I decided on significantly better resolution and accuracy and got some bench DMMs in parallel.