If there's one stuck in the bath I leave a piece of toilet tissue draped over the edge as a "ladder" overnight - it's invariably escaped by morning.
My house is home to many creatures and I never knowingly kill anything except slugs (ugh I hate slugs), which shows me to have shallow double standards, sorry.
One spider that came in this year was so big I could hear it's footsteps across my wooden floor, so yes, I do think they're bigger this year!
Pursley and Sly will pursue a spider until it's dead - even if this means camping out for hours by the washing machine/fridge/litter tray or wherever it has hidden. By morning it's usually upside down with it's feet all tied in knots, so I know they don't eat them (unlike bluebottles which Sly thinks are the tastiest things since dweemies).
I don't get involved as this is nature's way, but I wouldn't steer the cats towards any critter I'd spotted first.
The others aren't bothered about spiders in the slightest but they all, without exception, find moths irresistable.