My mother's laptop is kaput and she has no idea what sort of replacement she needs... and I can't really help.
She uses it for work (is self-employed) and needs something that works fairly fast - all the usual Office stuff, downloading lots of documents and pix, wants to be able to watch video and edit pix (so something that can run photoshop without crashing while doing something else at the same time?).
And preferably something that is easy to use and understand for a non-geek...
I have a Toshiba Portege (think it was an R400 but there are more recent models/specs). It was a lot of money but I bought it because of its excellent fast processing power. I run quite a lot of memory hungry analysis programmes. But mostly it is small, thin and light (about the size of an A4 pad) and less than a kilo)
This makes it excellent for what laptops are supposed to do: I just chuck it in a normal decent sized bag and go... I have had others and TBH I would always pay more for something very portable now.