There shouldn’t be any problem with your stored procedures, views, etc.
If needed you can set the compatibility to SQL 2000, but it’s usually not needed.
There is no need to create a new database on the SQL 2005 server and then restore the SQL 2000 database over it. Simply restore the database backup, SQL will create the database for you.
You are correct, DTS will require the legacy tools in order to edit and run the packages.
As always I recommend doing the upgrade is development and QA first, to be sure that there are no problems.