Primary market research:  Involves interaction with individuals, generally in form of an interview (though some of this work is increasingly being done online, but the high-value research is still conducted through in-person interviews with individuals who have volunteered to participate in the study).

Secondary market research:  Analysis of existing resources to answer specific question that is facing your business.

How to pick a firm for primary market research and manage the project?

1. Look for a firm with a history of work in that specific market segments because it can then leverage its credibility to open doors (particularly important in B2B type situations) and knows where to go and how to get the best results.
2. While these firms are typically good at collecting and compiling data, they rarely have expertise in analyzing and drawing insights.  Look for a strategy firm to do this for you.
3. Assign a project leader from your team to closely monitor the performance so that the research can be modified as initial results start to pour in.  That is why it is important to find a company that knows how to work intimately with the client's team.
4. Interviews are increasingly hard to perform these days, particularly with the busy schedules of senior level executives.  Do not insist on a certain number of interviews or with certain individuals in the marketplace.  Set realistic expectations so that the firm is not motivated to cook up research.  It is much better to have even one or two good interviews with industry leaders than to randomly call 25 of them and get replies in a minute or two that can actually be misleading.  We suggest that you contact a few industry leaders to arrange the interviews but let the consultant speak to them so that you get a different perspective.
5. We do not approve of anonymous surveys.  Always tell the consultant that they disclose that you are the client and paying for the research.  In most cases even your competitors will talk.  There is nothing embarrassing about conducting market research.

How to pick a firm for secondary market research and manage the project?

1. Strategy consulting firms are ideal for secondary market research.  Consultants at these firms have expertise in analyzing massive amounts of data to draw meaningful conclusions.  They typically do not have enough primary research experience and generally do a lousy job except for interviewing client executives.
2. Again industry knowledge is helpful so that the analysts can appreciate the context of a data set.  If you hire the strategy consulting firm for its functional expertise, make sure that you put an industry expert on the team.  This can either be an executive from your team or another industry consultant.
3. Make sure you provide enough resources to the consultant so that it can access all published studies.  If the idea is to rely only on secondary resources, you want to find out everything.  In any case, the rule of thumb is to validate findings of one study with at least two others.  It is perfectly fine to talk in terms of ranges rather than absolute numbers when there is discrepancy (which is very common when forecasts are involved) but being able to tap into several resources is key.

A final note on market research relates to how you use the data.  No market data is ever accurate so you should use it with that in mind.  Secondly, do not get married to a forecast.  Most of the time forecasts are guesses of industry executives and mean nothing.  Statistical forecasts rely on past data, and thus, are incapable of predicting the future.  So take any market study only as a guideline.

Related:  How to interpret market research data?   Market research project design proposal format

How to make the best use of business forecasts?