The most popular way of designing a web app with OOD/OOP is to use the Model-View-Controller pattern. To summarise the 3 main participants:
Model - I'm the stuff in the problem domain that you're manipulating.
View - I'm responsible for drawing and managing what you see in the browser. In web apps, this often means setting up a html template and pushing name-value pairs out into it.
Controller - I'm responsible for handling requests that come in from the web and working out what to do with them and arranging with the other objects to get that work done.
Start with the controller...
Views and Controllers often come in pairs. The controller accepts the HTTP request, works out what needs doing - and it either does it (if the work is trivial) or delegates the work to another object to do. Typically it find the view that's to be used and gives it to the object that's doing the actual work to write output into.
What I've described here corresponds with what you'd expect to find in something like Ruby on Rails.
Making lots of objects that you use once is certainly a concern - but I wouldn't worry about that aspect of performance up front. Proper virtual machines know how to manage short-lived objects. There's plenty of things you can do to speed up a web app - and I would start by sacrificing the benefit of clear organization for a speed up that might not even be the most important optimization...
MVC isn't the only way to go, there are other patterns like Model-View-Presenter and some really unusual approaches like continuation servers (e.g. Seaside) - which reuse the same objects between HTTP requests...