How to run Whonix conveniently and securely is one of the bigger issues of the project. There are big advantages and disadvantages to every approach.
This is really more of a “which lightweight linux distro should I use?” question. It will depend on your skills and familiarity with that distro, as well as your hardware requirements. I don’t think it’s a good idea to worry about file size of the distro: It’s easier to buy a large USB stick than to fiddle, fix, and be frustrated with a mini-distro you’re not comfortable in or lacks features.
If you insist, maybe try Slax (Slackware based, 210 megs) or Puppy Linux (runs everything inside RAM).
Any distro will run virtualbox equally well (I assume), as well as support full disk encryption (though some might come with tools that make it easy to set up – I don’t know which ones).
Tell us how it goes.
In the future, if we ever get whonix running inside QubesOS, I suspect that using QubesOS will be the definitive way to do this.