I will try to answer you in order:
1. You don't NEED an underlayment, but probably a moisture barrier. Personally I would still use an underlayment specifically designed for LVT. There are a few available which are fairly inexpensive.
2. For click, the thicker the better (usually), but more importantly go with a reputable brand with a high quality construction. There are countless articles on this subject so I won't get into it. For glue-down, 3mm is fine (usually). It doesn't need the heft since it becomes part of the structure once glued (if that makes sense?)
3. We're loyal to the brand we sell and believe it to be the highest quality and best value on the market. I would be happy to explain why, but I'm sure you would prefer a non-bias opinion! I'm here to help, not to push our products (which is why I won't mention the brand).
4. Price does not matter, but quality does. Things to look for are:
a) wear layer thickness - 0.020" is commercial rated, most brands range from 0.010" to 0.040", more is better.
b) base material - this is seldom advertised, but luxury vinyl is made from at least 3 layers. PVC (clear protective layer on top), image layer, and base layer. Please note this is a simplified explanation, the construction is quite a bit more complicated, but it should do the trick for your purposes. The base material can vary, and I would suggest looking for one that has good resistance to moisture.
c) image quality, sheen, & texture - this part is simple. Make sure it looks real!
5. Not a problem for a high quality product installed properly. A level subfloor is very important. I would recommend using a self leveling concrete. It's an expensive route, but will give you the best results. Dricore (which was recommended before) is also a great option, as long as you can spare the extra height.
6. You got it! This is personal taste, so, personally I would use a lighter color because dust doesn't show as well, and it'll brighten up the basement. Don't let me influence you though, use whatever looks good to you!
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Leveling , thickness,underlay
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