A business portrait has two key elements. Firstly we want to see the real authentic person and secondly, it must respect the brand of the business.
In terms of branding the location or background is key. The background needs to support the branding and appeal to the target market for your product or services. For example, if you are a corporate finance company selling to other city businesses then a clean blue background, blurred showing the outlines of a corporate office building may work really well. If you are in real estate or architecture and your market is consumer residential then showing part of a home in the background makes sense.
The use of colours is also worth considering with your market and brand in mind. For example, middle aged women tend to prefer the colours, green, teal, turquoise, purple and lavender. And men prefer blue, green and black. Blue being a clear leader, and purple being a definite no no! As well as looking at having the right colour to appeal to the customer, branding colours of the business can also be introduced. This helps to make the portraits enhance the overall branding on the web site.
As well as colour think about tones and shapes in the background, even if they are blurred. A legal company may want something along the lines of sandstone building, with pillars which gives the impression of longevity, established, stable, trust worthy etc. A tech company may want something more modern with clean lines. Each case should be influenced by the market you want to attract and your overall branding.
So what to wear?
T - shirts with writing on is not a good idea, as the writing is most likely going to get cut in half for certain head shots. If you are going to have a T shirt, or any shirt with a logo on it, then consider how long the logo has to live. IE If you are going to change the logo within a year or two, maybe best to do the head shots without logo shirts.
Patterns and thin stripes are issues for a lot of cameras and computer screens. There is whats known as the 'moire' effect, where thin stripes and patterns cause a secondary rippling effect. It makes the image very noisey and detracts the viewer. When converting to black and white it can look a mess and again detract the viewer.
If you are going to have some portraits in black and white then consider tones of the colours you are wearing. A pink tie on a pale blue shirt may look good in colour, but when concerted to black and white they are of very similar tones and blend together as light grey. Think of contrasting tones for better black and white portraits.
Casual or formal? This is dependent upon your target market. What would they like to see? What makes then relate best to you? This is likely the first time they have seen you and the start of building a relationship. People will judge you in less then a few seconds even though they have not met you.
Clever use of background, clothing and colours will help to establish the first right impression.