The best software for composing, recording and notation

I’d like to hear opinions about what would be the most simple and best way to write (notated) scores for pop / rock bands, classical / jazz ensembles and orchestras and create good audios "at the same time". I would like to record midi-instruments (which could be notated "automatically" when playing) and add on top of it some real instruments (guitars, bass, drums, winds, strings etc.,) which I could notate in the same session, after or before recording.
I have Ableton Live 9 and Sibelius 7, but I’d prefer to work only with one program, since I’d like to edit the audio and notated score at the same time, to hear the good sounds and to see the score right away. The purpose is to create “demos” and a scores of my compositions for band members, artists and producers.

I’ve heard Logic Pro might be good for this purpose? Experiences? I might not want to buy a new software right now and therefore would like to hear other suggestions as well. Any experiences with Livescore or Musescore (with Ableton)? How about Notion with Studio One?
Is Garage band totally out of the picture? What’s the biggest difference between Logic and Garage band? I’ve understood they work in a similar way, so one option could be to use Garage band until upgrading to Logic. Please tell me about your experiences. This might not be the right forum for these questions, so any tips for other forums are useful as well!

You might check out Pro Tools. It's designed to work with Sibelius, which you already own.

Yeah, that's where I am at. I am researching which programs to use. It has been probably 9-10 years since I have used any. Thus, I am out of touch. 

There is still no good "all-in-one" option, and honestly, it's looking doubtful there will be any time soon.

Staffpad and Musescore 4 do their best, but they cannot do all the genres listed in the OP with equal competency.

In DAWs, what built-in notation software they offer (if they offer it at all) is not nearly as good as even Musescore. Exporting to sheet music usually requires a lot of clean up even with an entirely-rigid quantization. MIDI imports into a DAW require a lot of work to make sound as good as something recorded directly in. It is to the point that you're better off picking just one option if you want to save time and money.

Frankly: There is no shortcut to getting both really great playback via MIDI, live audio, AND real-time notation. Your best bet is to work in the DAW, and only do sheet music where absolutely necessary. Your pop/rock band should be able to read MIDI or figure out the part via an audio recording sent to them, and same for just about any other musician unless you're planning on doing a live recording that involves all of the musicians in as few takes as possible.

What most pros and semi-pros do in this situation, is divide the labor and outsource the sheet music to someone else.