I start mine on rats from the off, they only get tried on mice if they dont take rats, then i will try multis( all F/T)
If it is a male, I'm not too fussed if its a mouser, it just gets a bit much with the bigger girls, but at the mo i am lucky as all mine are F/T rat eaters apart from one who will not take anything but multi's.
Oh and as for rat size, a small weaner is about the next step up from a ex large mouse(well in the UK, you may have different names for certain sizes in the US, but normally 10-15% of snakes bodyweight)