Transferring files from old MacBook while dealing with kernel panic and where to buy new one?

Yesterday I made a post on here about my 2017 12" MacBook with constant kernel panic - took it to the Apple Store and discovered it's got faulty RAM.

I'd rather just buy a new laptop than pay the $500 repair and have decided on the new MacBook Air. I never backed up my hard drive and will need to transfer everything over while dealing with my old laptop restarting because of the kernel panic.

Factoring the constant/random kernel panic restarts, will I be be able Time Machine/Migration Assistant or should I stick to just transferring over small batches of files onto an external drive manually? If possible, I'd like to use Migration Assistant since that's seems to be the easiest option. Also, I've got thousands of tabs up on separate browsers - would I be able to transfer those over using TM/MA? I would assume there's no keeping them just by transferring over files manually.

As for purchasing the new MacBook Air, I'm interested in getting the model with the 2TB SSD which from what I can tell is only sold from Apple's website (not in stores), B&H and Adorama. Does anyone know of any other authorized resellers that carry this model? Unfortunately Google's shopping results weren't any help here. Amazon, Best Buy and Costco's websites aren't showing it at all.