I have an old Sekonic L28c2. What a great meter for incident readings! I never liked it much in reflective mode, but as an incident meter it is accurate as all get out. It doesn't like low light much. It will do surprising low light however. It is fairly small as well, but that is relative.
For reflective light I prefer a Gossen Luna Pro SBC. It is a bit larger than the Sekonic, but goes down to very low light levels. Even lower than the Luna Pro. It is a zeroing meter, which some think is an advantage. It also allows very easy selection of plus or minus two stops since it is a zeroing meter. What I really like about the SBC is that it is a system meter. I have adapters for microscopes (useful for ground glass readings), 7/15 degree readings, and 1/5/10 degree readings. I also have a flash adapter. You may not need all that. There are other adapters as well, but if you don't need them that feature would do you no good. Oh, it does incident pretty well too.
Even without the adapters, the low light readings are worth having the meter. It isn't called Luna Pro for nothing. As to being backlit, I am sure that is an advantage. But really, how much? Which of the cameras you have mentioned have led readouts for the shutter and aperture? If you need a small penlight to set the camera, you can use it to read your meter. I just doubt for the extra cost you will find that so necessary. But maybe it is just me.
As to your question of how meters work, must will take a reading of the light, either reflective or incident. You would have a setting for the ISO of your film. You then match the reading of your meter to a scale from which you can then read a series of matching aperture and shutter speed combinations. Choose one you like for stop action or depth of field.
If you look at FrankS's photo, it is probably easiest to see in the lower middle meter, which looks like the European version of the Luna Pro. On the dial, you see ASA/DIN settings. The needle is at a position over the yellow line which has numbers. Matching the number there by rotating the large round dial on the lower portion of the meter, allows you to get the combination of shutter speeds and apertures. It may sound complicated, but isn't once you have done it a time or two.
Anyway, you have gotten a lot of good suggestions so far. You just need to research what they do, how much they cost, and how big they are, then choose one. My personal recommendation would be the Gossen Luna Pro SBC. It reads very low light and uses a 9 volt battery. It isn't the smallest out there, but isn't that big and heavy either unless you add the spot attachment. It isn't a small pocket meter, but with lanyard, carries easily around the neck until needed.
But only you can choose, and you may end up like most of us, with more than on for what it offers that others don't do as well.