Even before your handshake, potential clients and business partners gain an impression from you based on how you are dressed.
Attribution: Flickr - Alex Eylar
There are 3 ways to go about dressing for success.
1: Dress for your profession
Imagine a graphic designer in a suit and tie. It is not really believable. Better when they have blue hair and cool jeans even if they are meeting people wearing suits and ties.
Attribution: Flickr - mac-filko
To show your professionalism you can project that you belong to that profession with the clothes you wear.
2: Dress like your clients
We are more comfortable with people who are similar to us and so it is useful to dress in a similar way to our clients. If you customer base are farmers you should look like you belong on the farm and if they are rich executives you had better spend thousands of dollars on your suit because they will be able to tell if you are wearing a cheap suit.
Attribution: Flickr - Eric Constantineau
3: Dress for who your clients want to be
Why do funds managers wear expensive suits and drive fast cars? It isn't because their clients are like this as well, it is because people investing money want to be the type of people driving an Ferrari while wearing Armani.
Attribution: Flickr - Chris Christian
Think about the start-up industry. It is populated by young cool tech heads who do their best to look like young cool tech heads, because that is what their investors really want to be themselves.
Bonus: Combo move
You can combine these, for example a graphic designer might wear a suit jacket to meet their business clients, but the make sure it is teamed with a cool shirt and designer jeans. A banker might wear a suit to show their professionalism, but if their primary clients are farmers then they might wear it with a denim shirt to connect with their client base.