Thank you for explaining it. I do travel a lot on business and because of the roaming charges I have a factory unlocked iPhone 4S and use local Sim cards most of the time. when I am in the US like right now, I use a Tmobile card only because AT&T will not sell me a card without a contract and I am not here long enough to make that investment worthwhile. The downside is that I only get Edge data but most of the time that is better than going without data.
What I do to have my home phone available is put my local Sim Card for my home country in my old iPhone 4 locked to my carrier and have roaming data turned off in that one. I use the Tmobile to make calls and receive them from US contacts and the iPhone 4 to receive calls from international contacts.
To address your question finally, I always keep all contacts from everywhere with a + sign in front which gets me international access in all countries, then the country code and then the local number. I keep my contacts list synced in both phones, iPad and 2 macs through iCloud. there is no problem dialing and reaching local contacts that way even though you don't need to, but it is convenient so that you can access those contacts from everywhere directly from your contacts list.
For example, all my US contacts are written +1(212)1234567, my UK contacts +44123456789, my French contracts +33123456789, etc. and therefore, theynworknfrom everywhere.
I guess I will now investigate whether Verizon will sell me a local US sim with 4G data to use in the US on a monthly plan or better still a pay as you go plan.