If you have performance problems with anything, always profile first (for example by running with -Xprof) before doing anything else.
MemoryImageSource is not the fastest way to do rendering because what you will basically do is software rendering. Most of the time people use MemoryImageSource is because it is compatible with java 1.1. (But, since you want to make an applet game, maybe that's what you want?)
Maybe you could benefit from a higher level 2D game engine like GTGE. It has most difficult stuff done for you already.http://goldenstudios.or.id/products/GTGE/
I haven't used it myself, but from what I heard it's quite good and easy to use and it has tutorials.