What's the best way to start Java applications on Windows 7?
Try Launch4j (http://launch4j.sourceforge.net/), its a simple jar to exe wrapper (actually wrapping the jar is optional). It should solve your Icon and Taskbar requirements. Its also capable locating installed JRE's (some configurable rules). The font problem I don't quite get, Swing should automatically use fonts depending on Windows settings, unless you somehow overwrite that in the JRE options or in code.
Java Web Start - I wouldn't consider distributing an application any other way, these days.
The user does need to have at least J2SE 1.4; if your applications needs a later version, Web Start will automatically download an appropriate JRE.
See the JNLP reference for the tags for desktop integration (shortcut and offline-allowed), and file associations (association). These are only supported in WS 1.5 though.
I personaly use Launch4j (through maven with the maven-launch4j-plugin to be even more precise), and I implement the system tray management from within my application... (See http://java.sun.com/developer/technicalArticles/J2SE/Desktop/javase6/systemtray/).