Would it be possible to install Virtual Box and Windows and after all it is done, move the whole image over to a USB stick and just let it runs from there? If it can be done, what would be the recommended size for me to put it on?
Yes, but it would most likely run like crap. Not because of the port speed, but because of the flash memory speed, especially for writes.
There are some flash drives out there that have some half decent write speeds, but they tend to cost a lot more than the average flash drive of similar capacity. You'll have to do your own due diligence to research which ones are best for that ... Ignore the speed of the USB port in the specs. You will want to check actual reviews of them and compare the real-world read/write speeds. IOPS are another story... Those will be abysmal compared to the internal storage in the rMB, but still might be acceptable to you (they wouldn't to me.)
To get you started, I have had some good experiences, performance-wise, with the Sandisk Ultra Extreme II flash drives, but those are somewhat old now, and since then my general use for flash drives have been to use them for installing operating systems or booting live environments like PartedMagic for troubleshooting or utility use.
Those uses typically see the drives being written to when the image is initially copied to the flash drive. After that, it's reads from there on out. So I don't have a need for "the fastest" flash drive out there anymore, with respect to writes. The 3-pack of whatever Costco sells, for example, is good enough for me now ... 3 x 16GB for $25 last time I bought some, which is not bad.
In fact, TBH, you're better off getting a 128GB SSD and an external enclosure for VM use these days. Back when I used those Sandisk flash drives for it, SSDs were still prohibitively expensive, which is no longer the case (thankfully.)
Back on topic:
I don't have a rMB yet. Waiting for the Skylake "m" CPUs and to see if they add another port, but will probably get one when Skylake is inside, extra port or not. With that said, I will probably just use VirtualBox for running Windows. I have Fusion 7 Pro, but VMware raised the cost to upgrade with v8, which makes me want to puke. So, I'm sort of in a .!.. phase towards VMware at the moment. That may pass, given enough time, but for now, VirtualBox it is for me.