Local Data: Core Data hooked into a sqlite.db is the way to go. Some say it's a little heavy but I have had a lot of luck with it. It's going to give you everything you need to persist and query data locally on the device.

Remote Data: You pretty much have to go with a web service layer. The standard now-a-days is RESTful JSON. Directly connecting to a remote DB is too unreliable for the mobile world.

ASIHTTPRequest: A wrapper around network level API's for connecting to web servers. Use this.

http://allseeing-i.com/ASIHTTPRequest/