Hi,
Before you get too far down the upgrade road, be sure your firmware is up to date. Here's a cautionary thread:
http://discussions.apple.com/thread.jspa?messageID=1278725
A good link to memory was provided by NH Sullivan.
This Apple page:
http://docs.info.apple.com/article.html?artnum=58007
shows that 256MB memory will fit into each of the two slots (however, from experience almost everyone is aware that 512MB will go into each slot, and that two of those will operate nicely together)
Some further spec information about your particular iMac can be found at (not part of the Apple website):
http://www.everymac.com/systems/apple/imac/stats/imac_350.html
and also at:
http://www.apple-history.com/?
Battery part number is 922-4028 according to this Apple article:
http://docs.info.apple.com/article.html?artnum=86181
In the past they've always seemed to be available at Radio Shack, at a rather steep price around $12 or so. Available for less at a couple of eBay sellers - I buy from "ronaldo101" and get fast service.
Your will find quicker answers to your questions (many of which have probably already been asked and answered) about a slot loading iMac G3 at this other Apple discussion board:
http://discussions.apple.com/category.jspa?categoryID=133
In addition, the appropriate Apple Support area for your particular machine is here:
http://www.apple.com/support/imac/g3/
Have fun, and good luck!
Edit:
A how-to article I book-marked a couple of years ago:
http://www.macworld.com/2001/10/bc/howtoimac/