SMT is the main series. There are 4 entries: Shin Megami Tensei 1, 2, ...If, and 3.
All the other seires are there to compliment the main series and help add new features to it. The most popular side series are:
Devil Summoner - Devil Summoner, Soul Hackers, Devil Summoner 3
Persona - Persona 1, Persona 2: Innocent Sin, Persona 2: Eternal Punishment, Persona 3
Digital Devil Saga 1 and 2
These series are not connected at all aside from things the hardcare fans would notice. aside from the two Persona 2's and DDS', which ARE connected.
Starting with P3 is the best way because 1. it is completely different and enough to interest someone in the SMT series 2. it's not nearly as rare as SMT3 or DDS. 3. It's more story based than a traditional SMT so it'll be easier for someone used to other jrpgs to get into, thus, making the transition easier.
SMT games are like Final Fantasy's. They're like, never connected. There are things that universal in all of the games, like certain themes, certain gameplay elements (the moon cycles), but they are never connected story wise, aside from P2 and DDS1+2.