> I prefer that the VPS is managed as I’m not familiar with running my own server.
For $3000 you can easily get a managed dedicated server. I have a managed dedicated server with Liquid Web and I pay about $2000 per year.
For anything hosting related you should check http://www.webhostingtalk.com/ They also have a “Web Hosting Offers” section where you can get discounts for several hosts.
> a host that will allow the installation of Dropbox
Are you using Dropbox for deployment somehow?