My AVR is a Yamaha RX-V667 and I believe it does all those things you mentioned.
Yes - that AVR will do just about everything - except possibly handle the turntable. Phono inputs are disappearing from many AVRs. This will be the trickiest aspect of your system to deal with. I don't know much about turntables. Can you provide a model number? If you have regular Left/Right analog RCA outputs and they are amplified (this is the real question - I think most turntables don't amplify their output signal the same way everything else does - which is why devices used to have specific "Phono" labeled inputs which did some extra amplification).
For me, simplify means less wires and less remotes. I had a Universal Remote that did most of what I needed, but I now have Comcast's new x1 box and they said most Universal's will no longer work for it.
The whole point of a "universal" remote is that it can be programmed and re-programmed to adapt to whatever new gear you get. I really wouldn't listen to whoever "they" are. The Harmony line of remotes are programmed on your PC, using remote codes downloaded from an ever-growing library of codes. It's only a matter of time after a device is introduced to the public, for it's codes to become available. Like with anything to do with technology, increased flexibility comes at a price, and the Harmony remotes aren't cheap - but you already have the receiver, and the Harmony would be cheaper than the sound bar you list below.
My Samsung TV has enough HDMI inputs to handle everything (I think 5) video-wise.
As far as audio goes I have the turntable, maybe this can be plugged into a soundbar?
Here is one I was looking at...
Again - unless your turtable has analog R/W RCA outputs that are amplified, you won't be able to connect it directly to the soundbar.
I think it boils down to how important sound fidelity is to you. The problem with running all your inputs to the TV, then out to the soundbar (using a digital optical cable - if your TV has a digital optical output) is that all audio will be output as simple stereo (2.0). TVs are not designed to do any sort of sophisticated audio processing, so the "downmixing" of the audio you get from your various devices will not be as good as it would be in a more full-featured AVR. Will it sound "better" than the TV speakers? Definitely. Will the soundbar sound as good as using the AVR? Nope. Even if you use the AVR with just left, center, right and subwoofer (all the speakers can be in the front of the room in this case - to minimize wires) it will still sound much better than the soundbar,
This is what the AVR provides - added flexibility. You can always decide to add more to it later on, or update your speakers with nicer models if you happen to see a great sale.
The soundbar can be a perfectly acceptable solution, provided you understand and are OK with its performance and future expandability limitations (if you get the turntable connected somehow to the analog minijack on the back of the sound bar, you will have one remaining digital coaxial input available).