This store in Durham is actually an expansion of the excellent A&C SuperMarket in Raleigh. The A&C is the best and most affordable specialty Asian market in the Triangle area. Grand Asian in Cary is quite good as well, but somewhat overpriced and lacking in selection compared to A&C and Li Ming.
The hot food at both locations (A&C in Raleigh and Li Ming in Durham) is traditional Cantonese / Fujianese and very good and very affordable. What is curious about the Durham store is why they would have so much traditional American and Chicano options especially when Durham excels in Mexican offerings already and that Harris-Teeter, Target and Sam's Club are so close.
The Asian focus in A&C is a bit better than in Durham with more variety, but Li Ming has just opened, and on our third visit appears to show that they are resolving some of the differences between the two (especially the vegetables - which are excellent at both locations). Still, I am still missing some of the more hard to find Vietnamese options present in Raleigh.
I can't wait until they open the bakery! I think everyone should give this a go and experiment. For my wife (who came here from China a short while ago), she tells me that when she misses living in China, we go to A&C, now we're just happy we don't have to drive to Raleigh now!
(edited for spelling/grammar)