Altium and Eagle are great softwares for PCB design. The softwares can be used to generate schematics and this information (all the parts and connections) can be automatically transferred to a PCB design layout where the parts can be manually arranged and then automatically routed (for relatively simple layouts). Altium also has a simulator and a 3D design layout mode that is helpful for complicated design. Eagle does not have these functions. However it is much less expensive than Altium. Both these softwares are not free but are extremely useful for PCB designs.
For less complicated circuit design (where auto-route is not necessary) a free PCB design software called "FreePCB" can be downloaded from http://www.freepcb.com/. I have used this software during my AER201 course to design all the circuits necessary for the project including a PIC Microcontroller circuit, which was the most complicated circuit. Furthermore, it does not have schematic --> Circuit Board transfer of the necessary parts. Subsequently, using this software took longer than it would have if I used eagle but the software was free and it was relatively simple to learn and use.
Definitely for any circuit design Eagle is a great software especially with the auto-routing function, which definitely saves a lot of time during design. For example, you can use it to draw your schematics for your proposals and then during PCB design (if you decide to go this way), the software can transfer or import all the necessary packages (or outlines) based on the parts included in the schematics.
* For AER201 Eagle or FreePCB is strongly recommended *