If you're talking about minimizing parallax so that you get a clean stitch, there are a lot of tricks you can use like a hotshoe bubble level and a plumb line (aka Philopod) to make sure you rotate around the lens's no-parallax point that don't require a tripod and panohead.
However, distortion is another matter. Depending on how wide a field of view you're trying to cover with the panorama, distortion may be absolutely necessary in the finished pano, because a flat plane typically can't represent more than 180 degrees without some type of distortion. Which projection the panorama uses is probably going to have the largest effect on the final pano.
As for focal lengths, I shoot a Panasonic DMC-G3 and will shoot full spherical 360x180 equirectangular panos with a Samyang (Rokinon version) 7.5mm f/3.5 fisheye lens, so the distortion of the lens, to me, isn't really an issue, as both the member images and the final panorama are nearly distorted beyond recognition. But when put into a VR viewer, they'll look much more like rectilinear images.
As long as you have good stitching software that can handle lens distortion, and you're not shooting super-wide panos, it's typically not going to be an issue, as distortion can be corrected for. I use PTGui, but Hugin is a great open source alternative. Most people, however, would advocate using longer lenses to get higher-quality, lower-distortion, and high-resolution panos.