Do a search in the forum - there at least 2 discussions going on now about free PCB design software.
Unless you need to use surface mount parts, DIP & thruhole components can be mounted compactly using wirewrap and/or point to point soldering on perfboard on a similar size as a PCB. I regularly use expressPCB to layout my thru hole designs prior to assembly to see what will fit nicely on 0.1" hole space perfboards. You can get a bunch of parts to fit on a velleman ecs1/2 (60x80mm) perfboard, and even more on ecs1-h "island of holes' perfboard:http://www.vellemanusa.com/us/enu/product/search/?id=ecs
I can post some layouts I have done with expressPCB for wirewrap builds, I need to do it from home tho.
I have also used the miniboard service to create PCBs that held 48 5mm LEDs, 8 transistors, Rs, Cs, two 10-pin connectors, and two 7805s for an arduino to drive (two identical designs, I cut the boards in half to spread the displays apart).
If you need to go surface mount, then many here find eagle nice to use after you get past its learning curve. Search for "1284 eval" and scroll thru the first hit that comes back to see some current boards that use a 1284 processor in both TQFP and DIP variation to see what you can do with eagle. The free eagle-light limits you to 80x100mm and a single 11x17" schematic.
Another free option that comes up a lot is Kicad, I have not used it personally.