Apple does not allow trial software in the App Store. You can have 'lite' versions of your applications, but Apple requires that they are fully functional applications that do not expire and are not simply advertisements for your for-pay app.
Once you figure out what type of features you want to offer in a 'lite' version, one thing you could do to offer an in-place upgrade for customers in to use the in-app purchase mechanism. Apple now allows free applications to sell in-app purchases. So you could have an app call 'Foo' and inside 'Foo' you could have a menu option to unlock additional features, which would bring them to the in-app purchases dialogs where they could pay you to unlock more content of the app.
Check out Apple's tips & tricks for App Store submission: http://developer.apple.com/iphone/news/appstoretips/
There (listed on Sept. 18th, 2009) you will find a tip titled Just Right "Lite" that reads:
Using a "Lite" version to show how it
feels to use what you make and what
kinds of things your app can do is
definitely a good way to find
customers who will pay for the full
version of your application. But store
shoppers tell us it only works if you
follow a few simple rules:
- Make sure the functionality you decide to include is complete. Battles
that require weapons only available in
the full version, for instance, are
annoying and irritating instead of
enticing.
- Don't set time limits on your "Lite" version, either for run times
or life times. Applications that will
only run for a set number of minutes
per session, or that expire altogether
after some period of time, don't
recruit customers so much as leave a
bad taste in their mouths.
- Only display the UI for what your "Lite" version will do. Grayed out
menu commands, "more track/car
choices" you can see but not select,
etc. makes your "Lite" version feel
more like a commercial than a product,
and an annoying and ineffective one at
that.
- Do include information about your full application, including an option
to buy, in either your application's
About section or on the splash screen.
Just make sure the option to continue
using the "Lite" version is there as
well. A good impression lasts forever.
It's important to follow these simple
rules not only to create a better user
experience, but also because your app
will be returned to you by the App
Review Team for modification if it is
found to have time limits, incomplete
functionality, or disabled
functionality.
The most relevent part of that text for yourself and your proposed App design is the last sentence that contains "... your app will be returned to you by the App Review Team for modification if it is found to have time limits..."