Does anyone have experience in this area?
Yep, though I'm far from an expert.
What are your goals of the project? Everything stems from the answer to this question.
Example of goals: To make a business card for yourself and your team, To earn money from the series, to get discovered, to gain experience, to meet famous people, to build an audience, to showcase for a possible tv series, showcase for a possible movie, to build a crowd funding campaign/investor network. They all have different methods and different requirements and different costs associated. While you can have multiple goals from the list, if you do, it'll add complexity and increase your chance for failure, and some goals already require other goals to already be completed from other projects.
So I'm in the process of writing a story, one that will eventually become a script of 7 to 10 30-40 minute episodes.
Ambitious. I'd suggest cutting those episodes down to 10 minute range, if not less. Web viewers tend to have a short attention span. There are benefits to longer episodes though. It will increase your costs considerably.
One thing that'll happen is you'll get the shits that random internet girl with cleavage/cute pet will get millions of views from going viral where you have to work hard for each and every subscriber you attach and pay for high production values.
I was wondering if anyone could tell me HOW it would be possible to make a Web/TV series popular/successful? What process would need to be done, and basically
Make something that goes viral. Something that people just have to share with their friends. Either that or have a huge (7 to 8 figure) marketing budget.
The best way to make it successful is to make a high quality product that has a large target audience.
Where do I go following the completion of a script?
To the rest of development and then into pre-production. Attaching the appropriate required elements to increase the chance of success and mitigate the downsides of failure. Once all that is in place, then move into production, then post production and then into marketing and distribution. Simple right? Aren't you glad you're involved?
Say 3 years down the line, I have a completed series (filmed, edited, done) What happens then?
You'd probably shelve the project and move on to something more current. 3 years is too long a production cycle, especially for a web series. It would be tough to get any sponsors on board for the next season as the pay off would be another 3 years away and the hotness factor would have dispersed.
Is it worth starting with a Pilot and finding interest?
In my opinion, no. Web series aren't like TV Pilot season.
What Rayw said is also very important and relevant. Marketing is a huge component. Ignore marketing at your own peril.