I've seen all the other answers to this thread, and they all work in terms
of finding the next empty row.

I did want to answer the other problem you were finding...moving 1 column
over. As you found you can't add 1 to the letter and get the desired
result. Adding integers and strings never seems to work right...:-)

The way I move to another column is to activate the cell I want to move from
then use activecell.column + 1 to move over 1.

For example to move from B1 to C1:
Public sub moving()
Dim mycolumn as range

Range("b1").select 'This would not be needed if another part of
your code selected the cell
Mycolumn = range(activecell.column + 1, activecell.row)
Range(mycolumn).select

End sub

Now that code is untested and off the top of my head, so forgive me any
typos. But hopefully, that answers the column moving part of the question
for you.