All grinders are "messy" it goes with the territory.
I favour doser grinders over DoserLess, its just a personal thing and whatever you get used to.
Some grinders throw to the left more than others. A good example of two grinders pitched at the same market with same level of performance and quality, that differ noticeably in this regard are the Mini Mazzer, and the Macap M4 where.....the mini throws to the left more than the M4 so could be technically termed as being more messy. But as always it is up to the individual and what they get used to.
Live with a small paint brush and every operator should be brushing their spilled grinds away after each and every use. So I would say it is more in the operator training & understanding than the equipment.
Sticking strictly within the price bracket you mention, the best grinder I know of would be the Eureka Mignon either in doserless or doser form. Either way, go the brush and training.
very first CS site sponsor