Screen resolution ideas for my project

[Frikker]

I realise that this has probably been asked a thousand times, and I have searched similar posts to this but have not got an exact answer to my question. I leave tomorrow on a short business trip and am taking my laptop to work on my game but Wifi may be unavailable in the hotel so I really need to get an answer soon to aviod incredible boredom everynight in the Hotel on my own when I could be working on my project.
Anyway, shameful excuse out of the way , Im at the stage where I can start making my first background for room number 1, The game will have a similar art style to machinarium, and those who know the game will know it is quite high quality despite being scribbly and random.
My game will have a lot of detail, and fine lineart that will need to show. I wont be going down the pixellated path as it will spoil the atmosphere I am intending to create.
What I need to know is, what sort of resolution should I be looking for when I Digitally paint my backgrounds? It will need to be as high as possible without affecting performance.
Also when I play Machinarium on my 24inch monitor, the screen is always minimized to about half that and wont go any bigger to fill my monitor. Ideally I would want my game to fit full size into most monitors or at least not be cut in half on 22 and 24 inch sizes.
Any help would be greatly appreciated .
Thanks , Matt

[Monsieur OUXX]

I would say at least 1200xSomething. Or even 1600x1200.
There was a time when 1024x768 was considered "hi res", and that's probably the resolution machinarium was made in 6 years ago, but nowadays, on 24 inches screens, that resolution would be considered "cheap" by millenials

Also I've read somewhere that you should avoid 4:3 ratio for modern games, and turn to 16:9 ratios. I don't know what are the corresponding resolutions for that.

[Khris]

I'd recommend 1280 x 720.

[Frikker]

ok thanks to you both , I have something to go on now .
Oh and luckily I get Wifi in the hotel bar so you can get in contact with me if needed Monsieur OUXX, and ill be back home on Friday anyway.
Ill try a few quick background sketches at the resolutions you both suggested to see if the detail looks ok. But if anybody else has any input it will be a few weeks before I commit to anything in AGS. I just wanted to start test backgrounds whilst Im away and needed a rough idea of where to start. Thanks again .