Apply for green card after marriage: in the US or abroad?

My husband (US citizen) and I (foreigner) got married last year in California while I was visiting on a tourist visa. Since then I have visited several times and my tourist visa is still valid. We are planning to submit paperwork for my green card, and initially we thought he could submit paperwork from the US and have me wait in my home country while the process takes place. After talking to a friend who is going through the same process, we have been advised that it’s best (quicker) if I move to the US with my husband and start the process as soon as I arrive. We don’t want to do anything that’s illegal, and don’t want to jeopardize my tourist visa, so we would like to know if it’s in fact quicker to do it that way. We were told that if I’m in the US when we submit the paperwork, the process could take about 6 months, compared to about 2 years if I stay in my country. Is this true? Thanks in advance.