Think on Pagerank and page Title

Pagerank and page title are the two things you REALLY need to pay attention to. If a website with a low PR is ahead of a website with a higher PR it means their page title was more relevant. If you search in Google for "latest Seo Tips" my blog comes up #4 & #5. You can see that other websites came after me that had a higher PR. I actually have a PR of 3 yet I'm in front of them. This was partially because of my page title and keywords. If they did exactly what I did and had their PR they would be in front of me. Not to metion I also have the word "Seo Tips" in my domain. But if you search for the word "Seo Tips" in Google you'll only see websites with high PR. That's because that's a single word and lots of people are going for it in their titles and content. On "quality" keywords only the high PR sites will come up first. You can also search for the term "Seo". Don't you notice that all the websites on the first page seem to have about the same PR? As the list goes down their PR gets lower.

If I'm correct, your pagerank is based on the number of inbound links compared to websites that are in the same category as yours. So if my website was in a category that less people are competing for it would be easier to build up my pagerank. All because you have a high pagerank doesn't mean you can get a top spot for ANY keywords. Or does it?

It's based on the number of inbound links, their relevance to your site, and the PR of the inbound links you receive. There are probably other specs to the algorithm, but those are the ones most often talked about.

High page rank doesn't necessarily help you place high in the SERPs and low page rank doesn't mean you'll have poor placement. Placement in the SERPs also depends on what keywords you target for your niche and your on-page optimization.

If two websites are competing for the exact same keywords the website with the higher PR will appear before the other. The only time they have an advantage is when somebody types in a longer phrase. If the website with the lower PR has that phrase in their page title and throughout their website, they can beat the site with the higher PR if it doesn't have that phrase on their site.