"I'm not sure a table saw's rip fence would be able to get that close to the blade."Check the link given by Longshanks, then scroll down the page to the FKS/E table saw. You can rip 1/16" strips easily without fear of the fence getting in the way of the blade,but you will need to use the supplied table insert designed specifically for such narrow strips (it's but a 2-minute process to swap the insert). The other insert is designed for when you need to tilt the angle of the blade; it has a wider cut-out where the blade protrudes. Also the height of the blade is adjustable to suit the thickness of the wood which you intend to rip. No special blade is required - I simply use the supplied blade for ripping various-sized planks.
"...would I be able to make the same cuts on a band saw as I would on a scroll saw?"It depends on the thickness of the bandsaw blade. The intructions supplied with your bandsaw will tell you minimum and maximum radius cut per each blade thickness. Bear in mind that the bandsaw will not be able to make inside cuts - you will need the scrollsaw for that purpose.
Bear in mind also that any bog-standard cheapo bandsaw is ideal for most all general-purpose hobby work, but you are advised to bin the supplied blade and to invest in a decent blade (read more expensive). The supplied blades are usually of inferior quality and tend to 'drift', whereas a good quality blade will give you a nice, straight cut every time when the machine is set and adjusted properly.
When you get your drill press, the first thing you might consider is to install something like this:
http://www.rockler.com/product.cfm?page=10163... or perhaps a homebrew version, such as:
http://www.youtube.com/watch?v=LWn1lRTuOlkI can't offer any advice regarding the bench-type sander, other than this mini 12-volt version which is used for pruning matrix board, printed circuit boards and suchlike.