Have you got a warehouse or storage area?
You might be able to setup things there and make easier use of a neutral background (such as a white sheet/screen/etc...) which would make it far easier for you to take the photos that you want and have room to setup lighting and other items.
If not then setting up where they are sounds like the only practical solution.
You might want the book "light science and magic (I think its on edition 5 now)" as that will give you a lot of information relating to helping you control the lighting. Flash lighting can be done on the cheap or be expensive; but you've got to have an idea of what you need to make it work. Sometimes you only need one light; other photographers might take 10 or 20. So it can be quite variable.
A simple 3 flash setup might work best, though budget is going to be important. Wireless might be practical as its a store situation and you don't want cables all over the place. That will add to the cost but cuts down a lot on cable issues. Stands and then light modifiers.
Another option is a tripod and use HDR and combine various photos in editing to get the desired exposure. Requires more editing time but cuts down a lot on costs for lighting gear.
Note IKEA and some other stores don't even show photographs any more; its all 3D designs on a set all done in the computer because they've already made the 3D model to design the items. Of course this lets them do whatever they want.
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