Ah the Holy Grail for every business online or off. I want to be found by anyone wanting the services I offer in all the places I want to do business
As a small business, with, I would expect, a limited (cough) budget wanting to cover a relatively large area and large number of search terms (all the towns/villages in the area) I have the feeling that SEO will not be the way to go for you in the short/medium term.
Having said that, making sure that you have a good website doing all the right things will help (don't over optimise it though, keep it honest).
So, take a look at some of the advice floating around on here (there is a thread 101 SEO ideas or similar somewhere) or find a freelance on here to take a look at your site and advise on changes (I don't know any of them so can't recommend anyone) though I think you just need a 'review' rather than a 'service' - covering coding errors if any, canonical issues if any, content advice (page title(s), H1, H2, bold, emphasis), and some BASIC keyword research, some layout/conversion advice etc (A freelance on here may do that for free - or for a mention
on your site maybe - or for a relatively small amount; 2 or 3 hours tops for a reasonable, simple, report on a couple of pages I would suggest - unless they find LOTS wrong!!).
Once that is done it would probably be better for you to look at PPC (Adwords) - though I have only looked at 'babysitters oxford' and 'childminders oxford', I see that they are low search volumes and only medium competition, so the Cost Per Click for shouldn't be too bad. If you don't know Adwords/PPC already though, I would also learn the basics before you get into it to make sure you don't waste any money. Once again I don't think the ROI, or your budget, is likely to warrant buying in the services of professionals to set it up for you (though only you will know for sure and it may be a freelancer on here will PM you with a 'good offer').
In terms of backlinks, yes you want them, yes they should be quality, and yes they should be honest, so if you can think of good ways of getting people to mention you then great.
For instance, is anyone blogging about the cost of child care in the area? If so, could you write an interesting piece about how your business is helping keep costs down? If so, write it and send it to them - everyone knows that you are doing it for 'business' reasons - but if you write it well, and in an interesting, non-preachy, over-sell, way then they may use it as a guest piece and link back to you.
Is there a problem in the area with 'poor quality childminders', anything in the press recently?
If so, then write something about how you vet the childminders you use/recommend, how you keep testimonials on them etc and contact the papers to say that you would like to submit your article; or that you have it on your BLOG if they would like to use it, and see if they would interview you or link to the article 'giving the other side of the story'.
Do any of the child minders working through you have websites that they would be happy to say that they work through you on, saying how good you are at getting them work etc; and link to you? Asking for a link is fine so long as it is honestly given and provided in a relevant way.
The bottom line is, with backlinks the easy option (buying, directories, etc) whist sometimes cheap, and, well, easy, are ALMOST always the wrong option (ie relevant directories could be ok; back to my 'is the link likely to bring you business' point in the ealier post).
I could go on, but that's enough from me for now I think (for a long time I think having seen how much I have written!!!).
It is for SEO to get our website to appear higher in the google results. The reason being this is the main way people here about us. 
