Gmail for email - mostly because I got in way back when it was starting out and was able to get firstnamelastname@gmail.com
iCloud for contacts and calendars
This is exactly what I do. I rarely use the iCloud email address and have my firstlast@gmail.com set up as my apple ID. However, the ease of iCloud for Contacts and iCal has kept me from using google contacts or google calendar. I do like the gmail inbox options (starred, important, etc.), but wish the Apple VIP feature was available on iOS5 instead of exclusively for iOS6.