Firstly, i think it would be important for you answer the following questions
What are the list of things you need to achieve to make this a physical reality?
What knowledge, skills, expertise do you not have to get there?
Where are the people with those skills, attitudes, and experience found?
What compelling reasons do you have to convince someone to work with you specifically on this product? ie what can you do that others can't?
What is your ambition or objective with the project? Do you want to turn this into a company or do you want to just realise it physically for fun.
These are pretty fundamental to answer before you can proceed.
It really depends on what you want to do, electronic design is not (IMHO) much different then the ideas in software design. My background is EE, my day job is circuit design including firmware and in my spare time I do web projects, RoR mostly and some PC software and I think alot of the same principles apply.
There are many ways to design the circuitry as the same for software, many designs will be 'better' and many will be quicker to market. But you can hack hardware together just like you can for software (its just much harder to upgrade a circuit board design).
If you have never done much hardware design I don't think I would recommend buying a cheap microcontroller and going to town will all the design. It would probably be much more advantageous to get a development board and try things out first. Sites like sparkfun.com have a lot of different offerings. These also give you a schematic of the circuit to start with.
As someone else noted it really depends on your needs and goals, I am assuming this is something complicated enough to warrant a uC.
Great question, and there is always a fair amount of debate in this area. A way to start thinking about it is to ask how many logical states you need to store. If it exceeds a trivial amount you are almost always better off using one. I can't give you a more accurate answer without knowing more about what you are trying to do.
Then we have eliminated 1 design variable; you certainly want to use a microprocessor with usb support and lcd display capability. The ARM based at91sam9260 has that functionality and runs linux. Low priced ($6 in volume), it seems like a good place to start for you.
What are the list of things you need to achieve to make this a physical reality? What knowledge, skills, expertise do you not have to get there? Where are the people with those skills, attitudes, and experience found? What compelling reasons do you have to convince someone to work with you specifically on this product? ie what can you do that others can't? What is your ambition or objective with the project? Do you want to turn this into a company or do you want to just realise it physically for fun.
These are pretty fundamental to answer before you can proceed.