Just beginning to do a bit of woodworking. Can you guys suggest to me the most flexible, do most type of saw? Would that be a circular saw? Jig saw? Table circular? Table jigsaw? Cut off? Sawzall? radial arm? Band? I'm not sure where to start.
I currently have a hand hacksaw.
What type of woodworking? If you're talking about framing or building workbenches with dimensional lumber (2x4's etc) I'd say first a good circular saw and very (very) close behind a compound miter saw. The circular saw is the best tool for any 'rough' carpentry. The compound miter can be used for both 'rough' and 'finish' carpentry.
If you are talking about cabinet/furniture,etc, making, get a table saw. A breath behind the table saw is a jointer, and a few more breaths behind is a planer. (the furniture makers trilogy

)Once those are out of the way, look for a good router and use all those tools to build a router table, and you will be set.
You can spend lots of money on high quality, high tech woodworking tools. Your table saw fence can cost as much, if not more than the saw. (You get the picture) You may advance to needing/wanting those items, but in the meantime, invest in good measuring and marking devices. You may achieve efficiency using a good table saw fence, but you can get the same results with a board clamped to your saw also. (just an example) Learn how to properly setup and maintain your equipment, use excellent measuring devices for your setup, and mark your work piece properly for excellent results with reasonable equipment.
You're opening an entire different animal when you mention jig saws and band saws. They are more for making non-linear cuts, ie: circles, patterns, etc. Again, if you're speaking of finish carpentry/furniture making, these tools require additional tools to get the most out of them. These saws will 'rough' out your shapes, but you will need a drum, disc, and belt sander to finish them. Sawzall's are for DE-struction, not CON-struction. I've been woodworking for 30 years, and when I started thinking of type of fixed saw I wanted, I was initially sold on a Radial Arm Saw. I did some research and decided against. Due to all the moving parts on a Radial arm saw, they are
potentially much less accurate than what you can do on a table saw. You can do the same basic cuts on a RA saw, and dado's are awesomely simple, but I, again, decided for better accuracy from proper setup. I also feel that a table saw is safer than an RA saw. (I've had a dado blade ride the wood to the back of the arm, pretty scary, but I've also shot a few pieces out of a table saw

) Good Luck!