Dammit, i wish i saw this before you bought the flooring!
My experience with Shaw laminate in my old house with ANY moisture that gets left on the cracks (Piece of ice from the fridge, dog slobber, etc.) was bubbles that would form along the seams like the uppermost layer of material was lifting from the rest. It was the snap together kind. On the contrary, we had the old Pergo Select glued together kind in our master bed and bath which got wet all the time with no issues after 8-10 years.
We only used the Shaw brand for their vinyl planks for the bathroom. It's water proof. We immersed a small piece in water for like an hour and it came out perfect

The bottom is made from rubber, the top is vinyl. They are click-and-lock and floats. My neighbor used Shaw laminate and they had problems with it, too. Most of it was poor installation. I think the people they hired to do their floors didn't make sure their floors were completely flat. You can see it bucking up in a lot of places. Plus they did a piss poor job of spacing the edges accordingly. There are some places where you can see the gap past the quarter rounds.
For the house, we picked out Allen & Roth. It is 10mm with a 2mm padding. It's got an AC4 rating. It's really nice, actually

We bought a few small samples, locked them together, and poured water on it. We left the water on it for a couple of days, and no damage whatsoever. Also we didn't want anything that was glued because we want the option to replace planks if they get damaged....and with 2 dogs, 3 cats, and 3 kids, there will be damage LOL I would have preferred Pergo (which is what my mom has), but it was a whole dollar/sq ft more. We're trying to keep the cost low without going super cheap. The 10mm thickness makes a huge difference in how the floor feels and looks.
when i did my floor i used floor cement. i mixed it fairly soft then leveled the spots that needed fixing. BUT you have to replywood the floor after leveling. i used 1/4 inch mahogany or whatever it is they make as a substitute now. and screw it down good so your floor doesn't creak then your new floor. whatever you use to level the floor you still have to have a flat surface on top or any little ridge or lump will gradually come through. the better the subfloor the better the finished result. i layed coushion floor on mine. its been down 7 yrs. no issuses. if you use a leveling compound without putting a subfloor on top it gradually crumbles and makes a depression again.
We did study that option (as big diy'ers, we're also big researchers -- with limited budgets, we don't like to have to make costly mistakes if we can avoid it). But I read that those liquid leveller options are more for slight dips. We have dips that are 1/4 deep in some spots. I found this one long dip that is apparently along one of the floor joists that is too low. We considered pulling those planks up, slipping in shims, and putting them back in place, but unfortunately, they glued the floors down so it would break them and we'd have to replace them. I didn't want to replace the floors unless I had to because it would mean that as the new sheets settled, we'd get dips again anyway. Besides...despite the dips, the subfloor is in great shape. No mold anywhere.
The good thing about us doing it ourselves is that we take more care in how it looks because it's our house as opposed to a contractor who will come in, do it as fast as possible, without any care. My neighbor unfortunately has to fix their own floors because the company they used to install went out of business. I'll post pics when we finish
This guy had an awesome option to fixing dips without liquid levellers.