Can you help me to decide if I should install Geoserver, PostgreSQL and OpenLayers by myself or should I use OpenGeo Suite as it involves all these? I would need full capability which all these technologies offer when installed outside OpenGeo Suite and I would need to be able to host my own data.
The answer is 'yes' it provides full access to all packages for free. More details on the 'costing' page here. Whether it's better to install each application separately is a different question, and depends on your needs.
The Community release of Suite you can get for free has all the functionality of the upstream projects it is built from. The Enterprise release of Suite available with an OpenGeo support plan adds a few extra plugins that aren't included with either Community or the upstream projects, but the support is really what is being sold, not the software itself, so the Community release is not stripped or crippled.
The one caveat is that the upstream projects will be a bit more recent. A Suite release involves a bunch of extra testing to ensure that the particular versions of all the projects, and the various changes, tweaks, and configuration that turns it into Suite all work together on the particular supported platforms. You get a more integrated product as a result, but it takes time.
From my experience and reading the only reason I've found to install everything separately is when you need to run multiple instances for load balancing and related purposes. So if you want two GeoCaches running from the same GeoServer you want to install them separately. If you need multiple GeoServers, I'd install them separately. For most purposes its simply easier and affords better coordination if you use the stack. Whether one is better than the other is, as Darren said, totally dependent on your specific use case. If this is your first experiment then by all means install the stack and get to experimenting quickly. OpenGeo doesn't prevent you from customizing and controlling the settings on all the components. It just makes it easier and faster to get started while offering support and a couple of toolkits to help you get started, such as GeoExt. Have fun!