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Now your asking 2 questions there,
unfortanlley these 2 don't go together, There is eagle they do a freeware which is limited so that would be your cheapest option it is part Professinal.
But this all depends on how much PCB design you are doing, Do you just want to layout PCB 'S or simulate your design ?
Labcenter do a good product ARES(pcb)ISIS(shcematic and sim) but costly
then there is the top end package like Altium desinger and many others
So really it all depands on how much you want to spend.
I wish to do a maximum of four layers.
I want a maximum board size of around 30cm by 20cm
I do NOT want to use it for simulation.
I just want schematic capture which is linked in to a PCB Layout part.
I wish it to have a Design Rules Check and Electrical Rules Check.
I wish to be able to import certain PCB Layouts from other programs (eg PADS , Altium) and use them.
I wish to be able to import a PCB library component from another package (eg PADS, Altium).
I wish to be able to import PCB board shapes from mechanical packages (eg AutoCAD)
I don't want a limited number of nodes or components.
I do NOT want the schematic and PCB layout programs to be "separate"
Eagle would do what you want but only if you brought it has the freeware is limited to 2 layers and board size.
I would recommend Altium this has 1 program which does everything you require and more, eagle is 2 single programs not sure about Diptrace.
Altium is exspensive and has a hard learning curve but once mastered then so simple to do everything, The later version you can import step models so you can see your PCB in 3D also you can well in most cases get 3d step models of the enclosures and you can import that so you can see if your components or PCB will fit , This way you can build your complete design with out even atctualy building one in real life. Providing that your proto-type works of course.
Have a play with KiCad, I used it for some small things. To know if it has enough functionality and not too much problems, you have to try (probably you did already and look for something different now )
I don't think however it can import shapes from other packages...