From what I see it shouldn't take more than a month..

I would never go with an SEO companies.. they are gonna charge you hundreds a month for something you could do yourself.. Fiverr gigs are ok, but if you want to make a case study I'd guess you already have some kind of a process setup :confused: What I'd do with that kind of competition is do my own SEO, and than complementing with fiverr. Keep us updated!

Well that's the thing, I have a meeting with a potential client tommorow, but I have little experience in SEO results, I focus on the on-page SEO and website design itself.

What I need is to be able to tell the client "OK, so in about a month, your website should be ranked on the first page of Google for 'hairdresser town' and will be receiving roughly 50 visitors per month and about 10-20% of those should be making a booking'.

So you would say that the above paragraph holds relatively true for that case study?

I think the above paragraph is sensible. You might want to consider yahoo answers and a video for youtube too. These would get listed much quicker and support your main site.

Must be a small town with the estimated traffic only being 140 per month. Even at first position in the SERPs, you'll be lucky to get around 60 hits on the page per month for that keyword.

Give me a good site and i'll get it on page 1 within a week

It shouldn't take more that few weeks at most to get to 1st page, even number one. With that level of competition just proper on page seo is sometimes enough to get you there.
Just buy a few manually created links from high pr sites, there are some good services here at WF.

I would say it is less competitive, if you have done on-page well, and you have started building links then within 15 days you can see in good position.

The thing is there would be some authority sites which don't let you take over, this is the competition.

For a site having keyword in domain, on-page seo was done well and I was new that time in SEO, the exact searches were around 150 monthly according to Google keyword tool and it took my one month to be on the second position.

The problem was there were 3 authority site, one of them was forum and they were in top 5, so I had to build links continuously and it went to 2nd position, which was useless for me when I didn't see lots of visitors on my site... as I was not aware of keyword research, instead of selecting "exact searches" I selected the other one...