Upvote:10
The US is a non-visa national country which means you do not have to apply for entry clearance (visa) before you arrive. Instead, you have a landing interview with an Immigration Officer at the port. If your landing interview is successful, you will get 6 months leave to enter.
The landing interview will cover the points listed in Appendix V of the Immigration Rules. You would be advised to bring supporting evidence with you. The ones you listed will help. Because you were previously here on a T4, you should expect a more intensive landing interview because it may look like you are attempting to build up a life in the UK or look for work or possibly break the rules.
Genuine visitors do not stay for a long time because they have a life some place else. You should be prepared to explain how you will support yourself during your visit.
You can find Appendix V of the rules here.
Based upon what you wrote, a solid understanding of items V 4.2 is advised, particularly 'successive visits'...