I was wondering if I could install Fedora Core 2 striaght from the internet? Is the possible. And also would it be better to have Fedora Core 3, as some peole say its unstable

I think FC3 is fine but you can install FC2 in a similar manner.
Before you start, go to http://fedora.redhat.com/download/mirrors.html and write down the mirror which you want to download from. Also, make a note of the directory path which you will use.

You can do an ftp install if you have a high speed connection. You will at least need the fedora rescue cd which is about 76M and downloads fast. Burn that iso to a cd and boot up with that cd and type:
linux askmethod
english
us
FTP
select the network device

If you are connected to a router, use DHCP in the next step. Otherwise, you will need to know a vaild ip address and DNS server address.
[ * ] Use dynamic IP configuration ( BOOTP/DHCP )

Here's where you use the ftp site which you wrote down at the beginning. For example:
FTP site name:ftp://ftp.gtlib.cc.gatech.edu/
Fedora Core directory:/pub/fedora.redhat/linux/core/3/i386/os

If you typed everything in properly, a normal install will start, if you make a typo of some sort, it will pop an error message and allow you to make changes.