You might want to check out
Logisim. It's a schematic based logic simulator that will do you better for developing your own computers.
For real hardware, consider building with 74LS00 series TTL or 4000 series CMOS ICs. There's a fair amount of it available, retail and surplus. 74LS83, for instance, is a 4-bit adder in a 14-pin IC.
--Mark