I will submit your site to Google once only.
This is their recomendation - if you decide to try and submit to other ones or re submit to google again it may count against you and you may not be listed.
In my experience this is all you really need to do.
The rest tend to find you over the coming months.
(Remember the good ones WILL find you - if your website is configured to accept their 'spiders') - and yours will be configured correctly.
I ensure that your website has all the correct meta tags, keywords and descriptions as part of the initial development.
Also - If your site is a childminding website you will get listed on the www.little-sparkles.co.uk webiste - which will give you a very good start in the search engine rankings.
So really you should not have to worry about this side of things...