Yes you need an SD card, the instructions will tell you which SD cards the camera excepts. Or check the "spec's" on Kodak's web site for your camera. As you get use to the camera you may want more SD cards with more capacity (or more gigs of memory). These cards are getting cheaper every day. A lot less than buying multiple rolls of film, plus you can use them over and over.
I have a Li Lon rechargeablee battery on one of my cameras and they seem to last better than AA's. And yes the charger is in the camera. I would also get one or two "spare" batteries and keep them charged and ready to go when the battery in the camera gives up. Also a separate charger would be nice. But your usage will tell you if you need a separate charger.
I just went to the kodak web site...www.kodak.com and found in the kodak store some refurbished M341's. This may be a great way to save some money-check it out.