If you're using it for school work, then you'll probably be interested in Office compatible apps. You'll find several threads here that compare and contrast the various apps that are available. I use Apple's 'Pages' (Word compatible), 'Numbers' (Excel compatible) and 'Keynote' (PowerPoint compatible).
You'll have iOS5 on your iPad so you'll have a standard app for a regular and scientific calculator, so no need for that.
The basic Calendar app is OK too but it's somewhat limited in certain aspects. I use Pocket Informant HD, which sits on top of the standard Calender app. You can download the free User Manual from the Developer's website to check out its features. It's a very comprehensive calendar and task management application.
I'm sure other Members will come up with suggestions too, but use the Search button of the Forum and you'll find lots of advice, comments and reviews from our more than 120,000 members.
Great to have you here...
Tim