Which one is a sufficient studio flash setup for photography?

Two main reasons flash is used over continuous lighting.

Power. Lighting a scene for minutes uses much more power than lighting it for a fraction of a second. You may have noticed that most continuous lights need to be plugged in to a power supply, while most flash units work with small batteries. It may not make much difference if you're shooting indoors in a studio, but if you're out in the field and have to move around, it can get difficult lugging all that gear around.

Duration. A flash unit provides a very brief flash of light while a continuous unit is, well, continuous. A flash can freeze action much better than just using the camera's shutter. Try it yourself sometime: turn on the lights in the bathroom (and/or bring in your continuous light units) and take some pictures of a dripping faucet. Now turn off the lights and take some flash pictures of the same thing. See the difference?

Different lights for different effects. If you want the best color, and want to avoid harsh shadows, shop on ebay for a Novatron power pack and flash heads. Two flash heads and the pack can be had for under $200. Start making money before spending more. The flash heads will provide great color, allow for adding umbrellas to diffuse the light, and allow for shooting at lower ISO so you have high image quality. The flatheads also have flicker free tungsten modeling lights.

Red-eye is caused by the light from the flash reflecting from the back of the eye. There are several ways to eliminate or at least reduce the effect. One, as you've done, is to edit the photo after it's been taken. The red-eye reduction feature of the camera shines a light at the subject, causing the pupils to contract and thus reduce the reflection from the eyes.

A good way is to move the flash away from the camera. This causes the red reflection to go toward the flash, not the camera. Unfortunately, the D40x lacks the Commander mode to control remote flashes. Instead, you can use something like the SC-29 cord to move the flash away from the camera.

Another possibility to consider is to not use the flash at all. Bump up the ISO and see whether there's enough light for existing-light photography.

No I wouldn't say there is anything wrong with your DSLR I would think that the flash sync speed is set incorrectly. Each camera model will have a specific shutter to flash synchronized speed.
I've had and used SLR cameras with sync speeds as low as 1/30 and DSLR's at 1/250.
With my studio camera under studio strobes with a shutter speed at 1/60th I do get a slight blink of light BUT, it's the flash duration that makes the exposure.
There is also a difference between a flash made for a film camera and one that is made for a digital camera check make sure teat the flash is compatible with the camera you are using, also check see what the camera syn speed is and set your shutter speed to that. If your camera is equipped with an "M" mode then it also has a "P" mode for program this is a common mode to use flash because the camera sets everything for you all you need to do is compose, focus and trip the shutter. If the exposures are not coming out right then another thing may be a factor and that's the light metering mode (if you camera is equipped) look in your manual there could be as many as four different metering modes, check to see what the manual recommends for flash photography for your camera.

Another thing I use digital flash on my film cameras BUT not a film flash on a digital camera they just don't sync right.

Cheers

The glare is from the flash and/or direct source of light behind you or from the reflected angle. The only way to get a super detailed, glare free picture from a 90 degree angle of the surface is with no flash and all sources of light being soft, really bright, and /or indirect. Have you seen the large white inverted umbrella things on movie sets and such? That is what you need. Another option available, which I use on my ebay pics is to take it outside in the sun and take the pic from a slight angle. This gets the big fiery ball off the item and your shadow does not interfere. Cut yourself some slack because the pro quality pics of artwork are done in a professional photography setting like a studio or with lots of on site equipment.

You might be able to compensate for the flash from within the camera, under lighting. I've already found that setting it for fluorescent while using tungston works well, depending on what main colors you are shooting. Reflectivity can really change a final product.