Cheapest site for what? It is all going to depend on the part you are in search of. For example, Late Model Restoration and CJ Pony parts will often have really good prices on parts that can be difficult to find at places like Summit or JEGS. Late Model Restoration runs sales regularly. I follow them on facebook because they constantly post up "specials" or "deals"...of course, it is seldom something I need, but at least I know that should, for example, some hard to find sn part go up fr sale, I won't miss it...CJ also has specials, but I am not aware of any easy method to track them other than to occasionally check out their site...
Now, for more readily available stuff, Summit will price match. Plus, they sometimes have sales that are darned near impossible to beat. Last winter, for example, they had Trick Flow Twisted Wedge heads for less than $1,000. Plus, if you order from them, you may find they give you a "kick-back" in the form of a coupon...
American Muscle has really good customer service from my experience, and their prices are not out of line. But, IMHO, their selection is a bit more limited than Summit's...
Finally, if you are looking for routine maintenance stuff (brakes, hubs, lightbulbs, bushings, etc) Rock Auto is cheap. They do sell knock-off China made crap, so you have to be careful that you get what you are looking for quality wise, but their prices on name-brand stuff are hard to beat. And, they give a coupon every time that you order (usually five percent, and you can share it). I use them to order all maintenance parts (most recently pads and rotors for the wifey's mobile, axle shafts and hubs for my truck).
Remember also that Google is your friend. Search for the part, use the "Shopping" feature to find a part and part number, then use the part number to compare at as many sites as you can or desire. Sometimes the difference will be less than $5 across a whole bunch of sites, but occasionally you will find that one site has some parts for significantly less than others.