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Most of the time, I have looked up my parts before I go into the store, then ask them to look it up and then I challenge them when they get it wrong, then educate them on why I'm right.
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I usually call the parts store, check price/availability, and yes, try to always have brand(s) and part number(s) that is what I order by. We use Rock Auto much more than we buy from them, their web site is great for looking stuff up, easy to use. Always have Rock Auto up on the page for the part we are talking about, if the price is way out of line, mention that I'm seeing it for significantly less. I realize a brick & motor cant compete, but it's often good for some savings.
Because they have accounts at most of the same wholesale distributors as the local parts stores (for sure the two biggest ones here) what they list is a good indicator of what is available. Click "info" and some of the brands list alternate/OEM part number(s), makes lookup handy.
If there is time for delivery, thinking about ordering on line, I highlight the brand/part number, right click, search google. Price check Amazon, etc, sometimes Rock Auto makes sense, other times not so much.
We also use it when going to the pick&pull. Say a goal is a window motor, clicking on the part number brings up a list other cars that number is used on, often increases the chances if a nice part. Clicking on info brings up pictures, plug, gear tooth count, etc. Big aid in quickly finding the right parts.
That web site is very handy and easy to use, usually is up on the shop screen.