I fly helos (All of them) on MP a lot and in Blue Flag and DDCS at least, here's plenty of non-shooting flying to be done. In Blue Flag you fly crates around and unpack to set up defences, repair bases, transport troops to capture etc. In DDCS you have to sling load crates to set up defences and convoys etc. Very little shooting happens from helos (besides the KA50 and two of the Gazelle variants).
If you want to have the easiest to start and go, the Huey is the thing. You flip about 4 switches and it goes. It is quite slow though and is tricky to sling-load with.
The Mi8 has a bunch of steps to do to get it to go, about the same amount as the Ka50, but after a while you can do them in your sleep. ITO sling loading and general comfort, the Mi8 is the best one, and is my favourite of the transport choppers.