I don't know the link to it, but there's a quick video clip of Distilled's Tom Critchlow pointing out that "it's not about building links, but building relationships." I'd have to agree to a significant degree.
I'm not talking about buying relationships, but I'm talking about doing everything you can to get to know everyone and everybody in the SEO community who's good. Go to all the conferences where they "hang" and spend time going to all the "Link Love", "Search Love" and all the other SEO Love type of fests.
Also, find ways to build up "relationships" with everyone in your niche by either spending time where they spend time and get to know their needs. Cozy up to bloggers that blog in your vertical. Send them nice presents. Remember their birthdays. Build relationships!
With an unlimited budget, I would seriously spend a lot of it building relationships for your client.