There are lots of places to start when developing a web map.
If you have experience as a web developer, you should start by investigating the various services available to you that allow you to publish a map on the web. There are otherother questionsquestions answered here on this site that will give you valuable insight regarding the differences between the platforms available.
If you're starting fresh and don't want to commit to a particular platform, then address your business requirements. How are you going to draw your data on the map? How will the data be updated? Who is going to use this site? What will they do with it? Making these decisions early will help you assemble the pieces, or make choices that will support expansion towards a goal.
As for cost... I prefer to borrow a modern proverb: "Good, fast, cheap. Pick two." It's formally defined as the Project Management Triangle, which describes the balance between cost, scheduling, and scope to bring quality.