Under common UK and Scots law, anything found during the business of "beachcombing" is technically the property of the Crown and should be declared to the local Sheriff to determine its value. This includes stones, pebbles and shingle collected from any beach. In practice, so long as this is done in severe moderation (ie, a couple of pebbles, a handful of shingle) then no action will be taken against you.
If you collect anything at all from a "Site of Special Scientific Interest" then you are liable for prosecution, as these sites are protected against damage and destruction.
However, there is probably one specific example which you wouldn't get away with, in any moderation at all - the Stone of Scone. I wouldn't recommend trying to take any of that particular stone out of Scotland, the Scots would probably take issue with you doing so.
With regard to luggage issues, you should not have any problems at all - you can load your luggage down with bricks for all airport security care, so long as it doesn't trigger the usual detection systems.