Here's my advice on the matter --- I've been living in Zermatt since January 2005 and have climbed the Hornli Ridge myself:
First of all, you *definitely* need a guide given your lack of experience, ok we all agree there. Guides locally in Zermatt around around 1100 CHF. It's true you also have to do a "evaluation" climb with the guides - this is usually either part of the Breithorn Traverse or a climb on the Riffelhorn. Either is around 300 CHF additional as I remember. Go to www.zermatt.ch
and call their information line as they speak English well and can give you the exact details and the "official" opinion (of the guides, which isn't necessarily better, but is different from the view on a forum like this).
You can of course also hire a guide that is not local as others have suggested. But I think to hire a guide in Zermatt should also be fine. It's true they get a bad reputation, but they are extremely competent about getting your to the summit and back safely and I've heard that they treat their *clients* (as opposed to fellow mountaineers) very well.
You need to be in extremely good shape. Practice doing the equivelent of a 1300m vertical climb - perhaps on some local hills or stairs - as fast as you can. Over and over. The better in shape you are, the better your chances of not wasting 1100 CHF not to get to a summit.
Most people here are North Americans for whom the idea of being guided blindly up a peak is blasphamous. But it's very common in the Alps. A mountaineering course would of course be helpful and fun, perhaps, but not strictly necessary. The guide will handle all the technical bits for you. Of course, the more experience you have, the better your chances of success.
Do the Hornli Ridge, not the Italian Ridge. It's easier and your chances of success are thus better as a complete beginner.
Be prepared for loose rock - although it was far better than I had been warned - but definitely HUGE crowds. Try to plan your trip in shoulder seasons, if possible, such as early September (although you have to be careful since the first snow stops all guided climbs) as in July/August there is typically more than 100 climbers on the mountain each morning. The guide will handle getting you there without worry, but the crowds will make it unpleasant. Just bewarned but do it anyway since it's an amazing mountain and an incredible feeling standing on the top.
I am not sure what gear you need to have when climbing with a guide. Probably you need a good pair of mountaineering boots (costing around 300 euros, probably) which you have broken in and are comfortable climbing with prior to coming to Zermatt. As well as serious, good quality outerwear including Gore-Tex jacket and waterproof ski/climbing pants, various fleece and thermal layers, very cold-weather gloves as well as thiner mountaineering-type gloves. I think you can probably rent the rest of the gear in Zermatt (try Matterhorn Sport).
This is not a climb for those afraid of heights. Throughout almost all of the climb, and especially more towards the summit, you will have a sheer drop of more than 1000m vertical on either side of you. You will probably be lowered on a rope by the guide over a sheer vertical climb part of the during the decent. You want to be sure you aren't going to freak out by the exposure before you pay the 1100 CHF.
You almost certainly need adequate insurance including helicopter rescue for this. It may be included with the guiding contract, best is to call them and see.
Generally speaking, the climb should be fine if you have the above gear, are in EXCELLENT shape, get lucky with the weather (you need clear skies and sun on your summit day), and can pay the various guiding fees. I think it should be a great experience and not dangerous for you (contrary to the other views expressed here). Have a great time and let us know how it goes!!!