Your group should prepare a survey of the literature most relevant as background for your project. This work should be shared by all in the group and should be performed early in the project work so that it can inform your work. This should be updated for the final proposal.
A literature survey has much in common with a summary, but it takes a broader view. A literature survey generally takes some sort of perspective and then draws connections between a set of papers and that perspectives, using them to illustrate and deepen ones understanding of the perspective. In other words, it is important that you tell a story in your literature survey, rather than simply listing a long list of papers. Papers may contribute through enhancing theory, demonstrating applications, and so on. Often the writer will argue that there is a gap or a need of some sort that is not filled by the literature, alternatively, the contribution of the literature survey may be a new way of framing and/or organizing the knowledge about this topic.
To accomplish this, practically speaking, most literature surveys have a significant number of references. I can't tell you exactly how many to aim for -- just as the quality of your result matters more than the time you put in, the papers you choose to cover (and how you cover them) matters more than the exact numbers. That said, here are some examples of numbers of references: Many CHI papers have 20-30 references; a recent final lit survey for PandT had 32 references; when I write a grant proposal I usually have over 100. Typically I've read 3-5 times as many papers as I actually reference. I've attached a survey and that culminated in a journal paper to illustrate both the starting place and a possible ultimate goal, as well as the PandT final survey.
In writing your survey, you should be aiming for an integrative review (a summary of what is currently known about a topic). But keep in mind that while I helped define a topic area (e.g. end user programming), you still need to pick a topic (e.g., "End user programming for finding information in educational contexts", or "pitfalls and successes in evaluating end user programming systems" or so on). In other words, yes, it is appropriate to focus on a subset, and in fact I want you to focus on an aspect of this that is relevant to your own interests/research. This will also help to differentiate you from the excellent review you already found, and allow you to make use of the work they did at the same time.
Here are some other links that might be relevant:
Some secondary benefits of literature surveys
This kind of process is an important form of networking, background research for a PhD thesis, and generally benefits research. Once you've done this, you know who to try to meet at conferences, where to look for possible new work, and when you want to, say, sponsor a workshop on a topic, or find a summer internship, you've got the right contacts/people to invite. And it helps you to see where your own work fits in and how it is different. Always think about papers from this perspective as you read them.