Wow... You are very brave that you want to turn this into your very first PCB :-)

Do not underestimate that PCB design takes a lot of experience if you want to get a good result. There are lots of factors you have to consider, plus you have to be a real PCB CAD program jockey. Basic knowledge will not cut it I'm afraid, neither will a one component at a time approach. If I were you, I would start on much simpler PCB projects. I would say it will take you years until you should want to attempt turning a circuit like that into a real life PCB.

So.. That said, what then? Give up? Never! The circuit you show can be built on something which is halfway between a breadboard and a real PCB: on a prototyping board. That is a ready made PCB with only a lot of drilled pads on it. You solder your components on, and use wires to connect the pins of the IC's on the bottom side. This gives you the flexibility of a breadboard, but without the spring contacts and big parallel pieces of metal which are responsible for the bad properties of breadboards. The end result will be pretty sturdy, although you will probably not want to publish any photographs of the back side :-)

For an example, look for instance on the Farnell website: http://international1.farnell.com/a2z/a2z-f...l?PAGEID=6, and then PCB/Prototyping board, and a picture of a project done on one of these: http://www.8052.com/users/ShaikhYasir/DaqCardm.jpg I think this is your best bet. I know I made a lot of circuits that way, also microcomputer ones. Of course don't attempt to build a 2.4 GHz Pentium IV on one of these, but I think you understand...

As for Steve's remarks to your circuit: it is a bit of an antique, yes. And it contains some design choices which could have been better, yes. But from your point of view, you don't really need to worry about that. You are a hobbyist, and you want to play with it! All I can say is that it will probably work, and that it will give you a lot of pleasure until the moment you are ready to move on to something more state-of-the-art. But until that time, by all means, go ahead with it!