Your question is too broad.
What's your budget?
Generally speaking, you might want to think about using a digital SLR, which isn't just a camera, per se, but a kit... Professionals often have one or more camera bodies that mate with one or more lenses and quite likely a number of other matched accessories (flashes, filters, tripods, etc.).
The prices for such kits range from hundreds of dollars to hundreds of thousands of dollars.
when looking at DSLR's take the time and decide on what camera body will work "for now" what lenses will work "for now" then make sure you can upgrade, in that you want to make sure the lens you have now will work on the next better camera body and you want to make sure the camera body you have now will work on the next better lenses.
When most people start out money is a big factor when purchasing equipment, as you start making money and can afford better equipment, you don't want to have to replace everything to once. You want to replace just what you can afford to replace and continue from there. It only makes sense that you gradually increase your business or else you will be out of business. There are a lot of people in other industries that buy more than they can handle and don't take into concideration any unforeseen issues like the economy, insurances, death in the family or an employee's family, taxes, gas, taxes, insurances, taxes, taxes, taxes, oh well I hope you see my point.
As Kodak is undergoing bankruptcy, I am not sure that it is a good choice.
Instead, I would recommend a product from Canon, Nikon, Sony, Panasonic/Lumix, and several other major companies' products, instead.
If a DSLR is not needed, or within budget, then I would look for a point-n-shoot, that offers control, rather than JUST a programmed shooting mode.
Also, as almost all point-n-shoots have fixed zooms, my advice would be to look for ones with the widest angle (shortest focal length) in that zoom. A 2mm focal length difference in the wide-angle, can be noticed, where 20mm on the telephoto end, will likely go totally unnoticed.
I would also look for a camera that has a decent macro capability (close focusing), as some product photography, used in graphic design, needs to have that capacity.
Now, if a graphic designer, Web artist, also needs to do Video too, then the lineup narrows. While most of those still cameras CAN do Video, many use some proprietary schemes for saving the Video. Those can make the footage tough to edit with most common NLE (Non Linear Editor) programs. That could be a major consideration, as well.
Lots to think about, and to consider. I understand why the OP is asking, though I do not see any response to the question, "What do you need to shoot?" That can be a critical question, and the answer to it, can dictate which camera many of us would recommend. As it is, we can only guess, or add personal reflections, based on what WE do.
Many professional graphic designers and photographers usually use digital SLR cameras such as the Canon 550D to take excellent, high quality photographs.But it may be tha case that you wouldn't be able to afford a camera good enough to take these kind of photos,However, that's not strictly the case as models such as the Canon 550D are much more reasonably priced that other digital SLRs and they achieve similar results.
Before you make the plunge, read some reviews and take suggestions from the forum. Don't aim too low when choosing a camera. I've never heard anyone complaining that the camera they bought is too good.
Don't rule out used and refurbished cameras from dealers and manufacturers.
Yesterday I picked up my Fuji X100 and it looks like it's everything I hoped for in a camera I use mostly for cruises and street photography. Working around the water a lot, my 2 absolute requirements were a high-quallity lens and a great viewfinder. The X100 has a really nice optical viewfinder, a high quality electronic viewfinder (as good I think as the one on the Lumix GH2 that I recently sold), and a reasonably good LCD finder on the back. I went straight from the store to Marina del Rey to try it at the California Yacht Club on a bright sunny afternoon. The optical finder was impeccable, showing a really bright framed image with the important exposure info underneath the frame (a first I believe); the electronic finder was fair since in bright sunlight it (just as my GH2) tends to go dark, and the LCD which was essentially useless as nearly all LCDs when faced with very bright sunlight and reflections off the water.