I have a website that I would like to replace with the new one made in magento.
Domain name should stay exactly the same. I would like to know how can you do this in shortest time possible.
Start with answers for following questions:
1) What is key features of your current store, does Magento have all of them? If some feature missed in out of box Magento, does exist module/extension to add this feature or you should to hire a developer.
2) Do you choose a theme? (you can check my theme YourStore)
3) What data do you want to move from old site to Magento?
4) Who can help you with migration tasks, how much it will cost?
Magento is costly to keep alive. First ask yourself - can I afford Magento?
Shopify or other eCommerce platforms might better suit your needs.
If you still prefer Magento then you need:
1. A hosting server.
2. A theme, premade or custom made from PSD design mocks.