I've never used Incredimail, so don't even know if it's web-based or a client program.
I believe Ubuntu comes with Evolution, which is like Microsoft Outlook in that it combines a calendar, mail client and contacts.
Another option is to try Thunderbird. This is also available for Windows, and is very popular. Made by the same people that make Firefox. It's just a mail client, but can use an extension called Lightning to add a calendar, or use another Mozilla program called Sunbird, which is a standalone calendar program.
Whenever installing anything with Ubuntu (Linux in general), it's best to get the things from official repositories (repos) first, and only from a website as a last option.
A repo is just a machine storing programs ready to download, that have been checked by the maintainers of Ubuntu, so are likely to be free of viruses, spyware, etc.
If you click System -> Administrator -> Synaptic package manager (I think that's the link) from the top menu bar, you will be presented with a list of programs and other items, available in the repos.
You can use this to download programs from, such as Thunderbird. Just search for what you want, read the description to make sure it's the right thing, and tick the tick box, and click update.
https://help.ubuntu.com/9.04/
There's some really good documentation there, that should get you started.
Some programs, like Skype, aren't open source so can't be packaged by other people (such as the maintainers of Ubuntu). With these things, you have to download the package from the website, as Chuck recommends.