I've used the
Nodal Ninja R1 specialist head mounted to a tripod:
You need to know the particular lens you will be using before purchasing the head because the lens bracket you need is specific to the lens.
I used a
8mm Sigma lens found on eBay (mounted on a Nikon camera - the lens works with FX and DX bodies).
I bracket each image and combine them using
EnfuseGUI (free software).
EnfuseGUI creates an HDR type image, but maintains realism - the effects can be very subtle, just giving you more detail in highlights and shadows without looking like a computer game.
To stitch the images I used
AutoPano Pro - very good and relatively quick and easy to get to grips with.
For final assembly of the image into a interactive 'tour' I used
Pano2VR. Kolor (makers of AutoPano Pro) also have a incredibly well featured tour creation program but it a lot more expensive than Pano2VR.
In Pano2VR you can add patches for directly above and below the tripod, allowing for the totally seemless view all around and up and down from your point of view. Just don't forget to take the images above and below you when on site!
It takes quite a while to get to grips with everything, and you'll make mistakes along the way but it is very rewarding when you finally get it right
I appreciate you may not be wanting to spend a lot of money on specialist kit, so I hope you get even more suggestions for other solutions.
Good luck, and enjoy.
P.S. If you're making the tours for viewing on a website I'd skip making Flash tours, pretty pointless now imo. Pano2VR makes HTML5/Javascript tours which are great. It also makes Quicktime tours, but again like Flash, I'm not sure why you'd want to.