Don't really think the 1jz-MarkIII(chassis) came in an auto. Manual will probably be the only option. If you're still considering buying the 1jz, don't worry about the vvt-1 since it's not applicable on the 1jz at all.
What you're thinking of is the 2jz MarkIV(chassis). I've heard of different stories about the 2jz w/ vvt-i and non. There will always be modifications that need to be done when you swap.
Best practice is to find a qualified shop, one that's done many swaps and specialize with Toyotas'. Also, buy a complete engine w/ tranny, ecu and so on.
You have a lot of searching to do before this can be possible. Search through this forum and you'll find a ton of information.