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We need to get our name out there and advertising is one of the (or a) ways we can market the City.

Below is the (or a) cost comparison chart for the most popular business magazines.
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"a" is impossible before a plural like "ways": "one of the ways" is the expression.

Below is the/a cost comparison chart ... (Either one is correct. Use "the" if it's the only cost comparison chart under discussion and there is no possibility that there can be another. Use "a" if it is simply an example of one possible cost comparison chart and there might be others.)

for the most popular business magazines. (You must have "the" if you wish to say they have the greatest popularity.) How popular? The most popular.
for most popular business magazines. (You must not have "the" if you wish to say that almost all such magazines are included in the chart.) How many magazines? Most magazines.

CJ
Comments  
According to me:
We need to get our name out there and advertising is one of the ways we can market the city
Below is a cost comparison chart for the most popular business magazines
Normally ' the' is used with superlative degree,and "one of "the' ways" is nomal usage.
 CalifJim's reply was promoted to an answer.