The server is not open yet. Choosing a game mode on first login is built and still being tested, so it is not something you can do on a live world today.
When that choice runs, it offers Regular, Ironman, Hardcore Ironman and Ultimate Ironman, and it tells you the choice cannot be changed afterwards. Group modes are not offered. Choosing an XP rate on first login is still planned, separate from this.
Ironmen cannot use the Grand Exchange. The game tells an Ironman: "As an Ironman, you cannot use the Grand Exchange."
The modes page describes each mode, including trading, the bank and what a Hardcore death does. Read that page for the rules. Treat the first-login screen itself as still being tested.