It almost certainly doesn't matter for branding. Normal people look past the www because it's so common. Putting your site on a subdomain gives you the distinct

It almost certainly doesn't matter for branding. Normal people look past the www because it's so common. Putting your site on a subdomain gives you the distinct advantage of being able to CNAME to whatever you want, since CNAMEs don't work well on a bare domain. Putting a redirect in place means that your branding and marketing can just have "example.com" and it'll just automatically work.