Stock trading web site

If you are referring to starting the actual company in the U.S., there are a large amount of legal issues. You will need licensed brokers, as well as a legal consultant to help with the requirements the SEC set forth. You will also need capital to cover the positions of your clients, they will want to be able to buy or short stocks, and shorting requires capital to cover their positions. I would probably start at the SEC's website for information on this.

Now if this is a website for a brokerage that already exists, they should easily obtain the ability to build connections to exchanges. These connections themselves are not cheap. You can use any secure database, as long as it is secure, but pretty much everything needs to be logged for time and sales investigation or forensics (if you get investigated by the SEC).

Basically by the vagueness of your question, I would suggest you are very far from building something that requires this much capital and risk. Study everything you can about capital markets. Most developers in this industry stay in the industry, and many developers try for years for an opportunity to get into the industry. It's very difficult to leap in with both feet. If you would like some recommended reading, I can probably compile some lists.