For the dynamic SQL approach:
declare @sqlnvarchar(4000)
set @sql =
'
INSERT INTO '+
case
when @PeriodType = 'Monthly'then N'Monthly_Summary_Data'
when @PeriodType = 'Daily'then N'Daily_Summary_Data'
else null end
+' (Column_1, Column_2, etc.)
SELECT
Source_col_1,
Source_col_2
FROM
SourceTable
'
exec sp_executesql @sql