Laptop for Lightroom Classic

I would agree that your budget for a decent Laptop that can perform in LrC is too low

And I would not recommend any of those listed.

that being said

• For the first one, it has an old GPU, just 4GB VRAM, might be too small (VRAM) and a bit old for AI in LrC. The CPU has a TDP of 35 W (relates to power usage/availability) , not sure if that is a bit low for higher LrC performance. Consider this Laptop as marginal. Do not look for decent performance when using AI in LrC.
• Second one, no GPU, consider that Laptop as trash
• Third one, apparently no GPU, consider that Laptop as trash
• Fourth on, no GPU, consider that Laptop as trash

For a GPU in a laptop, look for at least 8GB of actual VRAM. Do not consider a laptop without a actual GPU. The Integrated video control without a Descrete GPU is a factor in LrC performance. Some state (Adobe) are stating that 4GB of VRAM is fine for AI in LrC, Actual practice is showing something at 8GB or more is actually necessary for performance in AI. Remember that VRAM cannot be added later.

For the RAM in any computer, now days, start at 32 GB, go for more if budget allows. In a laptop, you normally cannot add more RAM later, so go for as much as possible. Some will state that 16GB is fine, Well that may be true sort of today, but that will not last.

I do not have a reasonable recommendation in terms of budget for your new Laptop.

OTHER MEMBERS; does anyone have any info on Laptop CPU's to avoid? Perhaps issues with Power ratings?? The TDP?

Today's Lightroom Classic requires considerably more computer horsepower than a few years ago. The idea of Lightroom Classic today on a $700 computer is, in my opinion, a bad idea. I wouldn't bother.

What hardware do you really need? For LrC: a relatively new and powerful GPU, like NVidia RTX 3060 or 4060, and a relatively fast CPU. 16 GB RAM. Internal SSD, plus a second hard disk (spinning disk is okay) for the photos files are also nice (Note: if you run other programs at the same time as LrC, these requirements could differ). Yes I realize that will cost more than you $700 budget.