My question is at what distance does parallax become negligible?
This is not only the question of distance, but of the interrelation of distance and incorrect camera positioning.
You can shoot miles far away and see parallax errors if you walk around between shooting the frames. You can shoot hundred meter away from tripod without pano bracket and see no error.
It is important to understand, that close objects alone do not cause parallax errors. The problem arises, when close objects appear in several frames. The problem can be avoided often by framing: make sure, that the close objects are in single frames.
There is very much to discuss about it. I would not start out with a pano bracket. Start making panos, first avoiding difficult situation (typically, indoor is not realistic without a pano bracket). You will see, that many panos can be made even hand-held. Even in cases, where the forground is close (this occurs very often), the parallax error is often invisible due to blending. This works well with nature. A brick-like pavement is the enemy of the panomaker. I stitched a pano just a few days ago, from the Rockies, hand-held, 11 frames. The foreground was very close (within a few meters), but no problem, except the darn pavement (see
http://www.panopeeper.com/panorama/Rockies...montChateau.jpg, I had to crop away the bottom part, but you can imagine, what happened there). Sometimes it is corrigable, often laborously.
ANyway, make some panos, and wait until you run into the parallax problem; then think about how to avoid it, and only later buy a bracket. It does not need to be that expensive. RRS is particularly expensive, and unreasonable: AFAIK the adapters are customized for specific lenses
at specific focal lengths. Zooming ruins it. Plus, one has to know, that the entrance pupil of most lenses changes with focusing, so if you need that high precision, which is offered by RRS, then you have to look for an adjustable one.
If you are serious about it, then start out with a decent stitcher: PTGui (expensive), PT Assembler (only $39) or Hugin (free, but I don't know it). All these are using the father of stitchers, Panorama Tools.
There is an excellent forum at PTAssembler, dedicated to all issues around panoramas:
http://www.tawbaware.com/forum2