HKJ
(HKJ)
3
They are all fine to measure voltage, but I would probably prefer the UT210E because it can also measure current very easily (The AN8008 may easily blow a hard to get fuse).
When measuring voltage it do not matter what probe you connect first. In a car it would be a good idea to get a black probe with alligator clip.
The battery do not really care if it is charged before or after. Connecting wires in a car is a question about explosive gasses from the battery, safe way is to connect + first and then connect - somewhere some distance from the battery. The gasses are released when the battery is charged, i.e. if you have just put a new battery in the car and not started it yet, there will not be any gasses, except what has not been blown out from the old battery.