....and searching for my targeted keyword phrases, in quotes, that come up on the first pages of Google what exactly am I looking for? Use of the same keywords or similar? Content? Overall easy use of the site? Backlinks? Page rank? All of the above?
You are looking for the results in quotes to be no more than 10,000, but under 5,000 would be ideal. I learned a little trick from Pot Pie Girl (one of the greatest internet marketers out there) She said a great method is to search this way: intitle:"keyword" inahcor:"keyword" (just make sure you put the quotes around the keywords and make sure there is a space between your last keyword and the inanchor This method will give you more accurate results to how much competition you have. I have used this method for keywords that were over 100,000 just doing a search in quotes alone. After I did what Pot Pie Girl suggested, I found the competition was a lot smaller and I actually did rank for my articles.
What you are looking at is basically your competition. Those sites on the front page are the ones you need to beat to get your site listed there. So what you need to do is research each site and see what it will take to beat them. There are many factors to consider and many ways to beat them. For example, if the site has 1,000 backlinks but no other SEO is done on that page, you have a good chance of beating them. Most people will just look at the back links not realizing that the number of backlinks shown is only one of many factors Google uses. Also, they don't know how many of those backlinks Goolge counts as valid.
zeek is correct, it's not just backlinks that count. Onsite SEO and unique content plays a major part also. Often you will find that sites have the top 5 positions because they were a best fit even though they did not specifically target that phrase nor build backlinks with that phrase as anchor text. Searching how Jamie has suggested will give you a lot of information for this.