You are on the right track as far as customizing SharePoint's look and feel is concerned. Master pages are the right way to go. Through them, you can completely redefine the appearance of a site.
A master page defines "zones" (placeholders) in the page, where page layouts will then add/overwrite content. You must be careful to keep the placeholders of the default master page, because SharePoint expects them to be there for its own pages. It is possible to place them in hidden DIVs, but you risk breaking the capability for site authors to edit the content. When the site is seen by visitors, you are free to hide them all.
To have a "professional" look, you need a professional designer. Then you take this professional design and divide it into zones. There are places that are constant, so their content can be in the master page; there are places where the content varies depending on the context and this is where placeholders are useful.
Inside MOSS is a good book and has a chapter on branding a site.
You are free to use SharePoint designer for this purpose. Features/solutions are not a programmatic approach, they are a way of packaging changes to a SharePoint site for easy deployment. When you work with SharePoint designer, you are modifying a single site at a time. When you are happy with your modifications, which normally happened in a test environment, you need a way to copy them to a staging environment where users can test them. Then to a production environment. If you take the time to create features, then solutions, the deployment problem disappears. This is even "truer" in a multi-server environment where several Web front ends serve content.