Can I restore my regular iOS apps after jailbreaking? I'd like to have a go at jailbreaking my iPhone 4. I've backed up the phone in iTunes and transferred my apps to my computer, as I understand that the jailbreaking process is much quicker and more reliable on a totally wiped phone.

Once I've jailbroken the phone, can I then simply restore my apps, contacts and settings? If so, how? Also, can I still use the regular App Store on my jailbroken phone?
Yes, yes, and yes. You can essentially use just about any function of a iPhone exactly the same on a jailbroken iPhone.