All components are the 'through-hole' mounting type.
The LM324 - there are thousands, which one should I use
Search 'LM324N'. You get 12 hits. Digikey part no. 296-1391-5-ND would be my choice on cost and minimum order quantity grounds.
Noise pickup - please explain?
Lengths of wire from cells to circuit board act as aerials and pick up radio waves. Capacitors can be used to suppress the unwanted effects of these waves. One cap per strip board is essential and is connected directly across the power supply pins of the LM324. Hopefully the other caps would not be needed, so you should defer buying them until you have tested a prototype target. The caps are the ceramic type, radial, voltage rating >20V. (The higher the voltage the more expensive the cap).
Trimmers are single-turn, top adjustment, carbon.
Potentiometer is single-turn, top-adjustment, carbon, >= 0.05W.
Resistors: carbon, axial lead, >= 1/8W, 10% tolerance.
Terminal blocks: barrier blocks, pcb mounting, board to wire, >= 0.5A
Stripboard: Veroboard.
Those two batteries should cope.