SET Count = Count + 1 is IMHO the easiest solution..
More generally the concept of being able to get data, process it and while its being processed demand there be no underlying changes before writing the results of the processing is ususally not a reasonable one to have if you also require a scalable system.
You can of course do this and in many environments get away with it.. however these approaches will put severe limits on the scalaibility and complexity of an application before concurrency issues render the system unusable.
IMHO the better approach is to take an optimistic route and detect/retry if in the unususal case something you care about did change.
SELECT Count AS old ... FROM ...
.. processing ...
UPDATE ... SET Count = oldplus1 WHERE Count = old AND ...
Unless UPDATE gives you the rowcount your expecting you assume the data was modified and try again until it succeeds.