The cost of a website depends on what your needs are. If you are just starting up your business and only need a landing page for now with plans to expand later, this would cost less than say, an 8-page website with animations, API integrations and a multi-step form.
Yes, an arrangement can be made for smaller payments throughout the build. Typically, I request 50% up front and then the remaining 50% prior to the launch date. All payment must be received prior to the launch date in order for the launch to take place, no matter the payment schedule.
Typically, a website will start at around 4-6 weeks to design and develop. However, that greatly depends on the turnaround time to receive feedback from you, how many revisions you request and the features you’d like included in your website build.
Your website can be hosted by the host of your choice. If you enjoy supporting small businesses like I do, I recommend CyberBasement, however, if you choose a nationwide host, I would recommend WP Engine. I do not recommend GoDaddy, BlueHost or other big-name, cheap website hosts as they come with many issues including down-time, hacking, etc. Ultimately, though, you are welcome to use whichever host you prefer.