The Slackware site is definitely not the only place you can download binary packages. There are other sites, such as LinuxPackages
that maintain a repository of user-created packages.
As for installing packages from source, you really
shouldn't start with gcc. You should start with smaller and less critical applications that won't break your system if the compile/installation does not go well.
It is a matter of opinion, but many people feel (myself included) that you should not just install things from source without some method of managing the installed files. The best way to do this is to create proper Slackware packages out of the software you compile. There are a number of programs to do this, the most popular (and arguably easiest to use) being checkinstall