My understanding is that you will need to unlock the phone. Also, from what I can find, you will only get "3G" (HSPA+) speeds in areas that T-Mobile has refarmed to work on the AT&T 3G frequency (1900 Mhz).
This map shows where 3G on 1900 Mhz has been found. It also seems that you will not be able to get LTE on T-Mobile with this phone (T-Mobile uses Band 4, the Verizon Note II appears to only support Band 13).
I have the $30 plan and use a combination of GrooveIP and Google Voice to get "free" minutes using VoIP. I'd port your current number to Google Voice, have T-Mobile give you a new number, and then have Google Voice forward the calls to your new T-Mobile number. Personally, I only use GrooveIP (VoIP) when connected to WiFi but have all my calls sent through my Google Voice number. You can also send SMS texts to your Google Voice numbers, though last I knew it would not support MMS texts (texts with video or picture attached).