How many decent backlinks do I need for a no competition keyword?

Hello everybody, I have a question. Sorry if this is in the wrong section. This is my first post and my first real attempt at ranking in google for a keyword.

I found a keyword that I think has low competition that I want to rank for.
The 3rd result in google has (2 page backlinks) and (2500 domain backlinks) and is PR 2.
The on page seo is not optimized for the keyword.
The keyword is not in the url, title, Meta description,Meta keywords, content...
Well part of it is, but not the long tail one I am aiming for.
Like, if the keyword I want to rank for was (Best dog training), The 3rd place website is optimized for (dog training). None of the anchor text of the backlinks is (best dog training), Its just (dog training) and other stuff...

So I made a New website with like a 1000 word article. I think I have all the on page SEO down.

My question is How many decent backlinks do you guys think I need to rank 3rd for this keyword and about how much time should it take to rank once I have built them?

By decent backlinks I mean non spammy from pr 2 or higher with not too many outbound links and a good anchor text ratio...

Also if this is considered low competition, would I need to make several tiers?

I know this is a very relative question But I just want to get an idea from somebody that has tried this before.

Thanks to anybody that helps me out with any info. I really appreciate it!

It is difficult to answer because it is up to Google to decide whether you rank or not. However, I think in your case 10-25 PR2 should do the trick.

Hard to give an exact number. In my experience, I currently have a site I ranked top 3 in google for multiple keywords, that are very low comp with about 20 backlinks, and 7 ~500 word articles. The only real competition for me though were sites like amazon, tumblr, etc... nothing actually optimized for anything close to my keywords

If the keyword doesn't have really any competition then your site should settle quite high with only the on page optimisation that you have done. From there you can determine the position and work your way up from there.

Thanks Illini,
Amazon is actually number 10 on the first page for my keyword but it has like 1 backlink and the page is not optimized for it. How easy is it to usually beat them. And how much time did it take you to outrank Amazon?
Thanks again.

Good on-page, plus a few (5-15) 2.0's with good content, and you'll smash it in no time at all