I have interpreted your question as wide as possible.
When interviewing, what is the appropriate clothing?
Your clothing (just as your grooming, well-kept beard, nose-hairs, long hair etc) communicates about you. It communicates:
- The effort and preparation you did for this interview
- Your fit with the company
- The type of person you are (i.e. are you willing to dress up for your job?)
You have a lot of different levels of formality here. When you are too far from what the interviewer was expecting, it raises questions.
- Being over-dressed raises this question: "This guy does not know our company culture very well. Will he fit into a more relaxed atmosphere?"
- Being under-dressed tells the interviewer: "He did not even dress up for the interview: is he willing to dress up for his job? Does he value this interview? Will he also refuse to dress up for presentations to our clients?".
This is why being over-dressed is less bad than being under-dressed. As an interviewer, it is very hard to ask point-blank: "You are not wearing a suit. Why?"
Let's now go over your different options:
Level 1: full business formal (dress shoes, suit, tie)
This is almost never wrong. It may come off as a bit stiff, but you can correct this in the second interview (when you know what clothes people wear). Some people are more stressed when they are in full business attire, this could be an argument not to wear this.
A slight advantage as well is that you can easily dress down. When you feel you are overdressed (before the interview, or in between two interviews), you can easily take off the tie in the bathroom. I have done this on multiple occasions.
Level 2: dress shoes, suit, but no tie
This is slightly less formal. I found it appropriate for long-term clients (people you already know), researchers (who will probably be in jeans/t-shirt), or PR firms. For a marketing or PR firm, the guy across from you will probably be wearing Level 3, so you are not that far from him.
Level 3: dress shoes, jeans, blazer and shirt
This is often what is worn in PR agencies. It shows a smart confidence. It still shows you care, because you wear nice shoes and a well-ironed shirt.
In general, I would only do this in two cases:
- You feel extremely confident and know they will see a perfect fit for your future role. Even then, I would not give you any bonus points as an interviewer. Your making an effort to wear a suit is more important than your knowledge of the standard attire at the company.
- You are applying for a non-client-facing role and do not like wearing suits
Level 4: regular shoes, jeans, shirt
This communicates one thing: "I behave badly in formal situations."
For some jobs, this really does not matter. For others, it really does. If it does, your attire will not be decisive. The interviewer will also evaluate your behaviour, your composure, your smile, the tone of your voice... In practice, people not wearing a suit generally fail these as well: speaking very silently, being very nervous, telling inappropriate jokes.
Even here, you should not wear a t-shirt. A shirt is the simplest choice, but a v-neck sweater&t-shirt would also work.
Level 5: ripped or washed jeans, running shoes or sandals, t-shirt...
This communicates that you are not willing to change your attitude to work in a professional environment. This will limit your employment opportunities.
Source: Interviews in different environments, both as interviewee and interviewer, including for a PR-like agency. Sales talks (which are like interviews, in that you want to establish a fit with your potential client) in different environments (guys in overalls, banks, small start-ups, marketing companies...)