A few friends asked me what web services I use to run my business, so I am writing this to point people in future.
To manage email, I originally used Google Apps. When I signed up, this was free for 10 users but now costs $50 per user for new accounts: http://googleenterprise.blogspot.com/2012/12/changes-to-google-apps-for-businesses.html.
I eventually found email not structured enough so built my own basic ticket system on Google App Engine. Then I came across Zendesk, which did everything my custom system supported and was better designed so migrated there.
For invoicing, I originally just sent an email with the price but quickly discovered companies require something more official looking. For version 2, I found a Google Docs template and then modified this with the client details for each project. This was cumbersome so I built a Zendesk extension to automatically generate the invoices from ticket details.
For someone non-technical, I would recommend Freshbooks.
For crawling, I originally used my home computer. When that became too slow, I rented an Amazon EC2 server but I found this overly expensive because they charge per IO operation and bandwidth. Then I tried several dedicated hosting providers and am currently on Digital Ocean.
For this website, I have used WebFaction for over 5 years now and several times they have increased the server specs and features while keeping price constant. My only complaint is their changing SMTP policy caused me to miss some client emails.
For sharing files, I use Google Storage. This is a similar service to S3 but I was given a year free hosting and it comes with a nice command line tool and web interface, so I have never considered migrating.
Basically, I would recommend to start simple and invest in a better tool when you know you need it. Your business will probably fail anyway! So don't spend your time configuring a helpdesk system before you have any clients.