Hi,

I'm planning a site collection mainly for document management and search.

The home page will contain search box and navigation links to document sites.

I build a demo environment in which the root site is search center.

Do you thing it's preferable to set the root as publishing and the search site as a son-site?

Does it matter at all? (actually I know I can set any changes in site features and in the master page also later but I want to be sure it's really doesn't matter which web template to start

I think it does not matter because your search will get result from your content source so you can create your search centre in either way.