I've a couple of batteries for my 20D, one's the original Canon, the other is a Jessops. The jessops is already wors than the canon one it was bought to replace. But I'm not sure I could justify the canon cost so I'd probably still find cheapies on 7ds.
For card speed, check the manual. I think the 300d will do what my 20d does, which is buffer to ram, then write to card, so you just limit the volume of sequential shots at full speed, it then drops down as you reach the buffer limit and it has to start writing to card. While many cards are much faster than the cam these days, many are not, and many cheap ones on ebay are badged as faster ones and are simply not capable. Take care, don't buy tat.