Here's an article I found about calendar syncing with an older Mac: http://support.apple.com/kb/HT2513
I'm thinking if you need the assistance of a newer Mac to use its iTunes from time to time with your iPad, you could always visit a nearby Apple Store and they would help you.
But generally speaking you do not need a computer to support your iPad. You can update software and do iCloud backups over the air.
Enjoy your new iPad!