I've been developing web and iPhone apps for a while and I usually recommend to first use the provided sharing mechanisms. They provide great flexibility and as well don't require your app to request permissions on external networks. Using the iOS SDK sharing components will also save you precious development time.
The most important part is the content that will be shared. On that side, make sure all the content has a unique URL, and can be properly consumed on all plateforms, desktop and mobile.
Pay a particular attention to the head meta tags of those pages. Open graph and Twitter tags are not optional anymore and help driver a better visibility on the networks your content is being shared onto.
Don't forget to track with an appropriate analytics tool how your users use the sharing module. Then you can evaluate the pertinence of building something custom.
Based on my experience in Apple design reviews and industry best practices, a rule of thumb for apps is to always use the native iOS controls whenever possible. The laundry list of why is long, but the general idea is this is the most seamless way to take advantage of every iOS update for sharing and it's been vigorously tested and proven before release from Apple. (With proper testing on your app's implementation of course.)
The documentation is pretty easy to find on https://developer.apple.com but you have to become a member. If you are unable to sign up, an easy way to see this functionality visually cataloged is with Teehan + Lax's latest UI docs. http://www.teehanlax.com/tools
Once you see the native share control visually, go to your favorite apps and industry leaders to compare and contrast. You may even want to create a spreadsheet with screenshots of each and detail the interactions before you make a decision. (Or it may be totally obvious.) It all depends on your app's feature set and needs.
As for web, it's wide open and more information would be needed before I could recommend an approach. I'm available for a call and I'd be happy to dive in with you.