I have a small business and have always got somebody to design the website. I can do website design and do lots of it but it's only ever so basic stuff - not even using stuff like tables.
The first Q you need to ask yourself is whether you want to maintain it yourself. For a business, you may well want to be able to add new products and change pricing etc. This may dictate the tool which you want the design to be done in. My original designer, 1996, used Hot Metal Pro (a piece of junk). Then he got a well paid job and didn't do web design anymore, so I got somebody else. He used Micro$oft Frontpage (a piece of junk, IMHO) which generated a pretty but an incredibly slow to load website with each page containing hundreds of little objects and inefficient HTML. Then this bloke b*ggered off as well (got a well paid job) and the next man I used I told I want it done in Dreamweaver (which I use myself for my simple hacks). He did that; did a good website but lost interest partway through (probably got a well paid job) and we ended up in a dispute over what the terms of the job involved; basically some (few) things he did were very tacky but he said they are impossible to fix.
In the end I got a friend (who works in the office 1 day a week and looks after all this stuff) to sort it all out and that is where I have been for 2-3 years now. It works well.
A lot of things have changed in the past few years.
M$ have stopped constantly modifying Explorer. In the past, a website would work with v4 but not v5 or with v6 but not with v5 and not with Netscape etc etc. This is a real problem if selling into the less developed countries; a lot of people around the world are running an old browser under win98, etc. and they can't load a fancy website which uses browser specific features (read: it works only with IE6). OTOH, there is now IE7 and for all I know this will generate a load of websites which don't work on IE6...
A lot more people have fast connections, so bloated sites are no longer the major drag they used to be. But again this isn't true everywhere; a lot of people are still on dial-up.
The problem is that it's very hard to make a living just designing websites, so a lot of the people that do it clear off the moment they get a "proper job".
So it's essential to tightly specify what and how it will be done, so the next person (you?) can pick it up. A website done in Frontpage is close to impossible to do anything with unless again using Frontpage, and a lot of designers (most?) don't use Frontpage...
You don't say what business you are in but I can tell you that nearly everybody appreciates a clean simple honest website, which loads fast, tells you what the company does, and has simple navigation buttons on the side. No java, no flash, no active-x, minimal graphics. And keep any graphics on the main page narrow (no more than a few hundred pixels) because wide graphics prevent the pages printing properly (the RH margin gets cut off) from IE; most designers don't know this.
Bank on the designer not being around in a year's time. Buy a copy of (say) Dreamweaver, install it on some PC, and make sure that the job finally handed over is sitting on that PC, the site can be edited, and the new version can be FTP's to the server. Make sure this is specified at the outset as the deliverable package. Make sure it all works before handing over the money (or all the money).
As for artistic input, most designers don't have this. If you go to a big firm, they will bring in a graphic designer to make it pretty (say sony.co.uk etc) but all those sites (that I have seen) are massively bloated, and the job is very expensive. £100k is not unusual for such a site design.