There are three costs to consider with your website: domain name, hosting & web design.
I can recommend an Irish hosting company for the domain name registration and hosting. There will be annual charges to the hosting company and you should budget for approximately €100-150 per year, depending on whether you have a .ie or .com web address, an SSL cert (recommended), back up of files, etc.
My web design fees vary considerably depending on the size of the website (number of pages), features required, etc. As an example a simple website (like this one) would be €395 and would include the license fee for the Avada theme (which I use to build the website).
For a quote please get in touch at email@example.com.