@Arsine0
I am sorry this was your first experience with guests. They won't all be like that.
But I don't see a listing attached to your profile. Was this your home, or someone elses?
It would be helpful to have read your house rules and the description and details of the listing before replying..... but here goes.
So let's point out a few things that may help or at least clarify.
Airbnb is not like VRBO - there is no actual deposit to claim funds back for damages. it is a gesture/ preapproval/token only and is used (or not) totally at Airbnb's discretion. And in order to claim money for damages you will need to go to the Resolution Center, contact Airbnb and follow procedures. (so definitely read up about deposits, damages and claims in the useful Community Help Guides available here in the site).
So that answers your dilema of whether to leave a bad review or claim on their security deposit.
And before we talk about the review - lets' talk about the behavior of the guests and the mess. Unforunately, there are lots of people today who believe that if they pay extra for a cleaning fee - then they are not expected to 'clean' the place before they leave. And even if you spell all this out in your house rules - it doesn't really help once the guest has left. So expect this to happen again. A dirty barbeque, a dirty kitchen, extra payment to your cleaners and a few spots of stain on the bedroom carpet will not warrant a claim to Airbnb. Just my opinion of course and I am not trying to be nasty or negative. Of course if you want to try yourself, you can contact Airbnb to discuss further, after you have read the help guide and proceedures and perhaps after some other hosts leave their advice/comments for you as well.
So how to avoid this in the future? No real guarantees - but certainly don't rely on guests' 'common sense' as to how to look after appliances and items in the property as you suggest in your post..... everyone has their own views and experiences and they will rarely ever match up with yours. But you can help yourself by communicating with your guest before they book (a nice chatty message why are they visiting, expectations, special requests, plans etc), and communicate again after they check-in (which should be done in person - a 10 minute walk around the house to show where everything is and how it works will be a very positive bonding experience and will help 10 fold with reviews after.......) and if they do not reply then telephone/text on their phone number (which you get on the confirmation email). And then try to have someone there or on their way when the guests check out - and let them know that you are always nearby (even if you are not) and to text if they need anything at all during their stay.
You will soon get a feel for guests who are sincere and will care for your property - just keep reading and learning and it will become easier.
Best Wishes and good luck with your future hosting.