The 2JZGTE is a heaps better engine... but for a Celica application then the 1GGTE is definitely better suited as it is smaller, lighter, and a legal fitment in most (all?) states.
You can probably pick up a complete ex-Supra 1GGTE half cut (manual) for under $2k... I paid that for mine and later got the impression they'd have taken a lot less... although this was about a year ago and they are getting harder to find now.
As for your question about the 'non turbo' box - I asume you mean the W58 - the 1GGTE actually comes with these from the factory. You'd be mad not to buy a half cut.