For each size, there are various optimisations - ones that cram in as much capacity (run time before flat) at the penalty of thinner metal and a lower peak current, ones that can deliver a higher current, at less capacity or those that have a long shelf life (low self discharge rate) versus capacity.
Now you need to decide how you will use and charge your devices - will they be charged and forgotten for weeks, or kept on charge until needed, and is your kit especially demanding?
Also be aware that some equipment designed for 1.5v cells that start new at 1.6v and fall to 1.1-1.2 when nearly dead sees a fully charged rechargeable at 1.2- 1.3 volts as half flat and will warn of low battery, even if it is really in perfect working order. It may be worth checking with the makers if 1.2v rechargeable cells are likely to cause issues..
almost certainly fine, and as an addition a car or van charger may be worth considering.
You could try the ones out of the the other meter in the kit you want to use, just to verify you do not get an erroneous flat battery waning.
You can buy various AA batteries in bulk at good prices, such that rechargables become more trouble than they are worth. I use Duracell industrial ones which wholesale are much cheaper than shop prices, or bulk ones from CPC for Radio Microphones. Sometimes I use 30 or 40 a day for productions, and the capacity is little different from the more expensive D* ones. I have tried rechargables and they take a lot of effort and time to charge and the life of the kit power ends up the same as a normal AA, although the advertised capacity may be more. This is as Mike says the voltage monitors don't like rechargable 1.2 nominal voltage. Equipment designed for rechargable batteries has a switch mode, wide input range converter from the batteries so that they may be fully discharged properly, which may not be there in older equipment.
The MFT knows which type of battery it has in it and I presume the voltage indicator adjusts accordingly. I constantly have a bag of old batteries in my van to leave in a recycling bin, usually the one at a Screwfix, it does seem a inefficient way of working. The number of batteries from smoke alarms is decreasing significantly as the new alarms generally have sealed batteries, the next biggest quantity of old batteries are from the testers, it has also dropped as the MFT has rechargeable batteries in it, so swapping over the batteries in the other testers seems logical as a green measure and as a cost saving in the long term.
I did have a try with Ni-Zn rechargeables a while back - the big advantage being that their cell voltage is 1.6V rather than 1.2V so a lot of equipment can function much further into the discharge cycle. I've mostly given up with them for the moment - partly because of the high failure rate after only a couple of dozen cycles (at least one of a set of four would seem to loose a lot of capacity) and partly because my local supplier (Maplin) is no more. It might be worth a look if you can find a source of better quality ones though.
That is I fear to be expected. But if it works ok on the NiMH - even if it says 'half full', you will still get most of the benefit - the discharge curve of voltage vs state of charge is quite flat until the last 10% or so. BUT will not get much warning, as the change from half -full to dead will occur quite sharply, compared to the primary cells. From the electronics designer's perspective it makes it hard to do an accurate battery indicator on NiMH cells, as voltage is not reliable, so when it really matters, then we have to resort to something more like an electricity meter, and integrate and record the current in and out.