We hire a home for a week, usually 3 times per year. We choose based on the detailed description/photos on the website and usually concentrate on the fundamentals/basics rather than "luxury" elements. But we're a 3 generation family, so our needs are very different compared to, say, a couple wanting a romantic break.
We look for practicalities, such as checking the toaster is 4 slices rather than just 2 ( a pain if six of you are having breakfast or beans on toast together!). Choice of bed arrangements, i.e. doubles that can be turned into singles and vice versa to suit who is sleeping in each room. Decent Wi-Fi (we now look for fibre/cable rather than BT copper - many websites have started to mention speed and coverage!). Ease of parking close to the house (loading unloading a car full is a pain if you can't park outside). Washing machine, dryer, dishwasher, microwave full sized oven are essential - we're more likely to book if they're decent named, such as Bosch or Miele.
That's the kind of thing we look for before booking.
When we're there, then it's a given that sheets, towels, duvets should be clean, without smells/stains etc. A selection of well maintained books/games/jigsaws is good (not your old cast offs that you throw in a cupboard and never bother cleaning/checking!). Curtains that actually fit the window, close properly and black out the light are also pretty obviously essential.
A limited welcome pack is a "nice to have" but wouldn't be a deal breaker for us. Maybe a small pint of milk, a few tea bags and a few sachets of coffee, sugar etc so we can make a cuppa on arrival and maybe a small pack of biscuits. Not bothered bread, wine, juice, jam, cereal, cake etc as it's personal choice/taste - it's highly unlikely you'd get what we wanted so we have to go shopping anyway. (But again, we're a 3 generation family so each have our own tastes/requirements).
As for dogs, sorry, accepting dogs is a deal breaker for us. We won't book anywhere that accepts dogs regardless of what precautions they say they make. However small, well behaved, well controlled, you can always smell where a dog has been. I really think that home owners need to get of the fence and either embrace them or not accept them. The market is big enough to commit one way or the other. There's no need to try to keep everyone happy by accepting them but putting restrictions as to where they can go, what they can do, etc.