It is quite rare for toilets to leak from the base, because the wax seals are really efficient, especially if you use the kind with the plastic collar that dips down into the bend. That being said, a true base leak is due to a mashed wax seal (you need to make sure you seat the seal correctly) or a cracked bowl. As RP suggests, the flange may be too high or too low to mate properly with the seal. That’s doubtful, if it worked with the old toilet…
In my experience water that APPEARS to be coming from the base actually comes from a leak in the gasket between the tank and the bowl (in two piece toilets). It’s easy to check this out. Put methylene blue or some other dye in the bowl and flush it. If it appears on the floor, you have a bowl or wax gasket leak. If it doesn’t appear on the floor, next put the dye in the tank and flush. If it then appears on the floor, you have a tank leak (and you may even be able to trace it where it drips down the bowl to the floor).
This sort of trouble shooting is a good exercise and proves that problem-solving in plumbing is just common sense and logic.