There might be different instore promotions. List the parts that you might buy and ask for suggestions and alternatives on here.
Keep them in the boxes that come in and pack them in the middle of clothing. Basically everything goes through the x ray machines all the time so there is no worry about. Primary danger is something or someone falling on your luggage filled with computer parts so a hard case would work best however it will be restricted and overhead compartments are tight. Depending on the length of your flight, I would just use a backpack and slobber on it during the flight while keeping it safe instead of restricting legroom by putting it under the seat in front of you.
Carry on: large backpack - it won't fit in the...