is updating statistics necessary?
In most cases the default update statistics option on is just enough but depending on your system, your workload and the performance issues, you may have to run the explicit update statistics.
how about reorganize indexes or just rebuild them?
The normal best practices for this in the industry is run reorganize if the avg. fragmentation level is between 10-30% and rebuild if fragmentation > 30%. The numbers I listed here are NOT absolute cut off but only best practises.
shrink database?
You don't want to turn on this option. Take the time to turn this option off as this can cause long term performance issues in the long run.
integrity check?
This is an absolute must to run periodically. What is periodically mean i.e at-least once in every week.
Make sure you torn of page_verify option to CHECKSUM like below if the database was created in versions prior to SQL Server 2005.
ALTER DATABASE DBNAME SET PAGE_VERIFY CHECKSUM
I don't prefer to use Maintenance plans for these tasks and its best to use SQL Scripts. I use scripts from Ola Hallengren and they work great and recommend to anyone out there. You can get those scripts from
http://ola.hallengren.com/