You can use constant lighting because products don't move allowing you to use a relatively long shutter speed (1 second or longer).
But, constant lighting is also ambient light so you can't use shutter speed and lens aperture to control ambient light exposure separately from the strobe light exposure with a single shutter release.
While most flash units have a color temperature that closely approximates sunlight, constant light color temperature varies by light type.
As long as the color temperature of the all the constant lights you use is the same, and you use a sufficiently sophisticated digital camera, you can set the White Balance to allow for the constant light source color temperature. Understanding White Balance
An additional color management option is to use a gray card so you can set the White Balance post process.
Indeed when maintaining product color is important use every technique you can. Tutorials on Color Management & Printing
It really depends on the size of the product. If you're shooting small stuff, then it doesn't much matter; if you're shooting larger items, what you may find is that the cost of the continuous lighting necessary to ligh something such as a vehicle is prohibitively expensive, and with it's much greater output, strobed light would be cheaper.
I vote for strobes. Your studio will stay cooler and your electric bill will be lower. The draw backs are that they cost more in the beginning, and after about 300 fires in an hour, you will be hunting for Aspirin.
Thank you tirediron and photospherix. Are there certain products that cater to continuous/strobe lighting? Thank you for answering and being patient just trying to get as much information before spending the money. The trigger for strobe lights do they come with the lighting or is that a separate item?
You only need to turn on constant light to set up, and then to make the shot.
As John mentioned the product size will have a bearing as will your need or desire to have a background that is darker than your subject, or your background needs to be lit at a higher lighting ratio than your subject.
You may want to brush up on the fundamentals of photographic lighting - Light: Science and Magic: An Introduction to Photographic Lighting
We can't say how many lights you need. You will likely also need a variety of light modifiers (softboxes, diffusion panels, umbrellas), some reflectors, some flags to block light spill, some black flats to subtract light, a good tripod - or better yet a camera stand.
We do not know what or what range of products you are going to photograph, and we do not know how those images will be used.
Learning how to consistently make professional quality product images takes a fair amount of time.
Someone already having a good fundamental understanding of how to do photography and general photographic lighting may only need a couple of months to a year or so to get to that point.
For others it may take a couple of years.
I've taken photos and understand the basic fundamentals of photography. I have a Canon Rebel DSLR and understand iso and aperture..
The products are backpacks. I was wanting to get professional opinions and insight to make the decision quicker and easy on purchasing the equipment.. Just needing the basics right now, then I'll get other stuff that you mentioned..
I think a strobe is more versatile so you could use it for other types of photography should you be interested. However, I think the main thing with color consistency is using a target for color profiling and white balance. With these tools it technically doesn't matter what light you use. Shoot the target every time the light changes and you'll get accurate WB every time. I use the ColorChecker Passport from Xrite. A color profile is not color temperature related but a way to restore true colors for a given spectrum of light. Without a color profile, you'll always be somewhat guessing with color and wasting a lot of time with sliders and settings getting color that you aren't sure is perfect. The color profile combined with accurate white balance automatically makes color perfect, no adjustments necessary. The rest would be subjective enhancements. These tools work best when shooting RAW. Also, you would need a calibrated monitor if you care about color accuracy and consistency.