New to Digital

The Yamaha is an excellent amplifier, and that includes the inbuilt DAC. Hence I fully agree with the suggestion to get a Chromecast Audio and use its optical digital output into your Yamaha. See here for a serious review with measurement data: http://archimago.blogspot.nl/2016/02/measurements-google-chromecast-audio_27.html Without spending a real fortune, it is hard to imagine you can improve on this, unless your listening room is huge and your speakers very inefficient. I use one a seriously revealing system and I am perfectly happy. It will be much better than the bluetooth connection.
The sound quality of MQA is controversial. I think there are legitimate arguments for the view that it is in fact worse, and not better than ordinary 16/44 redbook cd quality. In the US Tidal and in Europe Qobuz will give you a streaming source for 16/44 quality, and I would not worry about it: there is enough research to support the view that lossless 16/44 is as good as you need for a perfect signal. In fact, there are good arguments that even the lossy 320 kbs Spotify stream is indistuinguisable from full red book CD. I am not sure - I thought it sounded better on informal listening, but proper comparative blind listening tests suggest few if any people can really hear a difference (I could not under such controled conditions). Anyway, I would never spend a penny on MQA.
If you ever consider spending serious money, I would suggest looking into modern speakers like the Harbeth M30.1. Your speakers are about thirty years old, and that is old - speakers do degrade with age. Also, speaker technology has improved considerably. Speakers make a real difference. But for now, enjoy the digital age.

There is really no point in worrying about the quality of the Yamaha. See here for a test of the earlier AS700, identical but for the lack of digital inputs: http://www.avhub.com.au/product-reviews/hi-fi/yamaha-a-s700-integrated-amplifier-review-and-test-pag...
The results are seriously better than for many audiophile amplifiers costing perhaps ten times more. Its only limitation is the power output at around 2x100 watt rms. If you are using inefficient speakers in a larger room you may want more power. If not, you will be perfectly fine. Since the digital output of the Chromecast Audio has been shown to be bitperfect, there is no issue there either. I have not found any test yet of the Yamaha's internal DAC, but I would not expect anything other than excellent results.
So the only way in which you may be able to improve the sound of your system, is by getting really good modern speakers like the Harbeth M30.1. The rest of your system would be an excellent match even for such expensive speakers. But speaker choice does depend on personal preference, room size and music selection.

Enjoy. The digital output of the Chromecast Audio will certainly be a sonic improvement over the Bluetooth connection.
As for speakers, I am afraid they are expensive, but they also have the biggest impact of the system’s sound. But since you already have speakers, you can take your time to save and listen. Unless your room is very large, the Yamaha would be good to drive the Harbeth M30.1. They would be my personal favourite for a very neutral and accurate speaker in a still modest size. If your room is very small, move one size down to their P3ESR, if the room is rather larger, you may consider their SHL5+.
Harbeth's Alan Shaw is firmly convinced that expensive cables are a waste of money and designs and demonstrates his speakers with basic cable. Quad's genius designer Peter Walker similarly thought they were nonsense. Well designed speakers and amplifiers do not need anything more than bog standard.