Other than obviously the cheating state of matter like you imply, what aspects of MP you're looking for?
My rule of thumb is for reboot era CODs with official servers that guarantees searches to be fast enough, always get the latest one but always stick to it for maybe 3-5 years without buying whatever CODs released during that period.
Other than that, if you're okay with those whose live service updates are finished:
- MW19, the baseline.
- MWII, if you like it real slow movement wise
- MWIII, if you like it real FAST movement wise
- Black Ops Cold War, if you like OG classic movement and aim feel but also has modernized/retrofitted mechanics
Black Ops 6 and Black Ops 7, while they
Are indeed faster than MWIII, in the end of the day you will only remember you are having headache from numbing your mind for just to get some sick clips that don't even stimulate your dopamine as much.
Don't EVER consider vanguard. Don't even think about it. You will waste money into a game you ate not only going to be numbed with for no apparent benefit, it will bore you with lack of gamemodes and maps, and potentially hurt your ears with sharp, high pitch clicks audio when firing some guns constantly. It has also probably the least amount of players among all reboot, so lost of the time you're be pulling shipment and das haus. Gaming is always about wasting time AND having good time, not just the former exclusively.
For Any CODs before MW19, just see which ones are supported by third party launchers because their multiplayer services are actually better and maintained (if you're on PC, you can kinda ignore this if youre on console.). Additional trivia: MW19 is currently the only reboot era game that has proper third party launcher but no third party matchmaking servers or server browsers yet so you just gotta play LAN.