Batik is fine if you want to do SVG rendering, so long as you don't plan on fully interactive framerates. It draws to canvas pretty fast, but it's a real CPU hog when re-applying constraints after modifying your scene. I've used it for drawing large, complex diagrams that needed elements at multiple layers to be visually interactive at low update rates (in my case, I only needed about 4 Hz on sub-gigahertz PCs).

For a small game? I'd suggest sticking to the Java Shapes API and Graphics2D drawing classes for AWT drawing. It's quite capable, and has all the big problems solved for you already (like antialiasing, text rendering, fill algorithms, blending, etc). Set up double-buffering and go nuts.

If you want to start aiming your code to lower levels and doing more complex graphics work? Maybe set up LWJGL and work your way towards reproducing things like this: http://http.developer.nvidia.com/GPUGems3/gpugems3_ch25.html , an article that explores how to set up a pixel shader to rasterize one antialiased bezier curve per triangle, and use it to rasterize complex vector graphics in 3D.

http://stackoverflow.com/questions/1558852/learning-resources-and-tutorials-for-using-the-java-batik-library

http://www.svgopen.org/2002/papers/kormann__developing_svg_apps_with_batik/

Disclaimer: IIRC I used the latter article above as my own jumping-off point when I was learning Batik for the aforementioned venture, but my coworkers and I had to do a lot of experimentation on our own to get it to a usable state. I cannot share any of the code we did develop for it, as it is no longer owned exclusively by our employer.