So I've been meaning to ask (and may have before): if I've never played Shin Megami Tensei games, where do I start? I have my PSP and 3DS, so that's the big limitation.
There's not really a start because there's no storyline continuity between the games. They just have similar themes and system rules. Since you've played Persona, you already have some familiarity with the spell and weakness systems.
I've never played the DS version of Strange Journey, but I've heard good things, so I'm looking forward to the remake.
As for what you have access to:
Shin Megami Tensei IV is an experience. Though not without flaw, particularly in the characters, it's an interesting story and is often on sale for pretty cheap on the 3DS eshop.
That said, I've been told Shin Megami Tensei IV: Apocalypse is better. It's kind of a what-if story that shares SMTIV's setting but with a stronger story.
SMT: Devil Survivor Overclocked is one I can wholly recommend. It's a little odd in using tactical RPG maps, but within that are more standard RPG battles. Excellent story. It almost feels like a bridge between Persona and SMT thematically.
I can't help on the PSP front. Only Atlus game I played for that was Persona 3 Portable.