If you're going to take the toilet out anyhow, I would definitely run the laminate right up to the floor flange and put the toilet bowl over the new vinyl floor.
Also, if you can, fill any unnecessary holes in the floor flange and caulk between the floor flange and the new vinyl floor. That way, if there is any water leakage, it'll be onto the top surface of the sheet vinyl where you'll be alerted to the problem. If you don't do that, then any water leakage may very well end up causing plaster damage to the ceiling below or wood rot around the toilet floor flange before any water leaks are discovered.
If you put the sheet vinyl in after the toilet, the usual practice is to caulk around the base of the toilet to hid the cut edge of the vinyl. Then, if you do have a leak in the wax seal under the toilet, you won't know about it until the water starts to leak under the sheet vinyl and you get a purplish brown mildew stain under the new vinyl. Also because you won't see any water leakage, you may not take immediate action to fix the problem, and that's a situation conducive to the situation getting worse and wood rot setting in.
If the vanity is one that you won't be able to replace the vinyl without removing the vanity, then I'd fit the new vinyl around the vanity. But, it's not a big deal to install the vanity over the vinyl either.
