Hey, what kind of fields do you play at?
If they are heavily wooded areas you might want to avoid the M14. It's a Battle Rifle and akin to carrying a fishing pole in the forest. I have done that and it's not so much fun.
IMHO the AGM MP40 is wanting. I have had two of them. They are creaky and the shot per shot perfromance is horribly inconsistent. The Cyma Thompson is a better choice for a WW2 airsoft SMG. Besides that, the MP40 isn't the best to use when prone due to the long magazines.
I have participated in a few WW2 milsims in Ontario. I can barely recall anyone using an AGM MP40 in recent memory.
The MP44 shoots a wee bit hot for most fields. It has its' faults too (hop up and fastener issues come to mind immediately). But out of the three I would recommend the MP44. The hi cap mags haven't been much of a problem from what I witnessed at WW2 milsims. Most players only have one and fill it will the appropriate bb's.
Don't worry about that period appropriate nonsense either. WW2 airsoft is in it's infancy in Ontario. And besides that most of guys that have allied impressions are either 101st or British / Canadian Airborne. This makes the games ETO and Normandy or Post Normandy or "what ifs".
Given that the price point for these three AEG's is roughly the same I recommend you go with the MP44.
How the Axis AEG goes over with your Allied impression is another story