Either one would be badass, you can get a pretty damn strong 383 from the dealer, GM perf parts. Something like over 400tq.
The ls1 6.0L engine will be a nicer daily driver, that's debatable, it will however give you more mpg.
My ls1 lasted a hard 100K+ miles of abuse, and no smoking or knocking, you gotta love the ls1.
I haven't seen anyone do a tahoe swap. However, i did a pcm for a guy that put a 5.3L in a 4x4 truck, 95 model i believe.
You should be able to stay under 5K if you buy used parts.

what else you got on your mind,

allen