Hi Ivgi,
I'm responding on this thread rather than on the first one I responded to. I received the email you sent me and took a very quick look at your company's website. Within the scope of Q&A, I'm afraid no on can do your keyword research for you - that's a big process that will require an investment of multiple hours of time. What I can do is give you my honest take on your situation in hopes that it will help your company to make a good decision.
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I think there is a lack of clarity in the business model. I am not familiar with the online shopping business model and have not worked with this type of business before, but it seems to me that if your company only delivers groceries to two places, then you aren't just an 'online grocery delivery', you are in some way a local business. I'm not positive about this, but whomever handles the work for your business needs to totally clarify what the business model is. You've stated that you deliver to two cities. Then I see something on the site about nationwide delivery. Which is it?
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The website is not giving me any type of value proposition. Why should I be shopping online? Why should I be shopping online with your company? What is the value? How do I get groceries? Who delivers them, when, etc? The site isn't telling me.
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The website copy needs a complete overhaul. It appears to have been written by an ESL copywriter, and as the audience is likely to be primarily speaking English as their first language, the problems with the copy will not instill trust in the quality of the business.
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It may be that the overall architecture of the website needs to be re-done, and for sure, the company needs a clear strategy for exactly what they are doing. The front entry page appears to indicate that there are 2 different sections to the site, one for each city. But what about the nationwide offer?
These are just a few of things I see in my brief glance at your website. It is my belief that your company's success depends on hiring a professional SEO and Usability team to do a complete audit of the website and create and implement a strategy, based upon market research, that will enable the business to clarify is model, message and promotion options. If they are expecting you to do this in-house, and you are, as you say, a beginner, then the company's expectations are not on-track.
I would strongly urge the business to choose the very best firm they can afford. You need real pros to do this right...perhaps check out the list of recommended companies here on this website.
http://www.seomoz.org/article/recommended
I hope my suggestions are useful. I truly do believe that your company needs expert assistance with their online marketing and should not be expecting an in-house novice to get them results. That is too much responsibility to put on one staff member's shoulders, given the size, scope and needs of the website and the business.