For generic (e.g. non Arduino) parts the following websites are useful:
For example type in "74HC02".
Both of these will search through the listings of several distributors, including Mouser (usually the cheaper) and Digikey.
Giving you prices to compare, availability (how many in stock), minimum order quantity.
Make sure you check whether the part is through hole or surface mount.
OemsTrade is similar to FindChips but searches more distributors.
Try it and see what you get.
With a credit card and a ship to address you can get parts either fast
(overnight air, which is expensive) or reasonable (Ground, far less expensive.
Designing circuits and boards for people is my business so I use Mouser and Digikey a lot.