I have a sizzix bigkick (it's the same as the bigshot but it's blue ~ my inlaws got it for my christmas present and used a coupon at Michael's in Canada to get it).
As for dies ~ I really like Spellbinders Nestabilities
!!! They are a nesting type and you get a lot for the money you spend on them. I just got their daisy patch and the posy patch and can't wait to attach them to some alligator clippies. If you want flowers or circles (just check out what ones they have, they have SO many) that are the same shape but different sizes, nestabilites are for you. If you are anything like me and can't cut out a perfect circle, these will be such a lifesaver.
~ for the spellbinders dies I bought a piece of magnetic sheet at walmart and just attached it to a stamp storage page and cut out holes and they fit in a binder. The spellbinder dies are magnetic and this is a great way to keep them all together. I also bought a label maker and have what the sizes are on the page the die is on.
I have some sizzix and cuttlebug dies but I use them mostly for cardmaking and haven't used them for bowmaking. HTH