Highchairs: I did a LOT of research and ended up with... the £15 Ikea Antilop.
It is utterly fantastic. Totally easy to clean, packs down reasonably so you can take it in the boot when visiting granny*, can be used with or without a tray, and it just works. And if you find it doesn't, for any reason, you're only £15 down rather thank £quitealot. We decided to test the Antilop before buying something expensive, and we never looked back.
It doesn't turn into a kiddy chair as the child grows, but TBH you don't really need that. I can't recommend it highly enough.
*or splash out on another to leave at granny's.