Hello @meharahsanawais and welcome to the forum!
The standard_* montages in MNE are designed such that they immediately work when doing source localization with the fsaverage brain. This is why they look a little different from what you might expect.
You had the correct idea choosing the easycap or biosemi montages for sensor-level analysis. What you need to do first, though, is simply rename the M1 and M2 channels in your data to TP9 and TP10, respectively. (See Using contralateral referencing for EEG — MNE 1.5.1 documentation where they go the opposite route)
Then, you can set your montage:
raw.set_montage("easycap-M1") # or any other template montage
When plotting the montage, pass sphere="eeglab" and everything should look like you expect.
Best wishes,
Richard