Wow, you’re in UK? That does make things a lot more difficult because most sellers in USA will not ship to UK.
Okay for your TV setup, I would nix the idea of an HT Processor because it is going to be hard to find something that can ship to you within your budget. So:
- Emotiva AirMotiv 5s - $499 USD (check with Emotiva to see if they will ship this to UK)
- Audio-GD NFB-11.28 $330 USD plus shipping (they will ship to UK)
Alternatively, you could move up the DAC/preamp to an Audio-GD NFB-29.28. It is twice as much at $638 USD. However, it is a better DAC/preamp and it also has more inputs (for both analog and digital), just in case you need to expand. It depends if you want to spend the extra money.
Or you could do like mesch says and get a very low-cost integrated with some ELAC B6 speakers.
In addition, you will also need that digital cable (Blue Jean Beldon) and a set of RCA audio cables that are long enough to reach the AirMotivs (maybe something like 6 feet?). You can start with cheap cables initial if you want. Or buy something like the Audioquest solid-core interconnects.
-----
Regarding your vinyl/dac system, the challenge here is that the availability/shipping AND the UK exchange rate is going to kill you. For local stuff, you can try looking on the Ebay “UK” site (https://www.ebay.co.uk/). I see several integrated amps from Ebay “UK” that I would put on a list:
HEGEL H200 Integrated Amplifier USED - £1,499.00 / $1,969 USD. This is only an integrated amp with no additional phono or DAC. It is the most powerful of this short list and the Hegel is known to be very refined sounding. The Hegel will likely be the best out of this list, but you would have to buy both an external DAC and phono preamp.
Parasound Halo Stereo Integrated Amplifier DEMO - £2,195.00 / $2,884 USD. This has everything built into it already. Parasound is known to have a lot of punch/slam (maybe even more than Hegel?). It’s a great starter platform, but you can always expand/improve by adding external DAC or phono preamp. This DEMO on Ebay UK is actually more than USD Retail, so if you were interested in this one, I would just buy a new one from Audio Advisor in the USA (they will ship to UK as long as they ship to your credit card address). It may be hard to find a used one that will ship to UK.
- Arcam FMJ A39 Stereo Integrated Amplifier NEW - £1,699.99 / $2,232 USD
- Arcam FMJ A39 Integrated Amplifier USED - £849.00 / $1,115 USD
I included two, one used and one new, so that you can see a range. The Arcam will be very sweet sounding and easy to listen to (it is biased into Class A to 20 watts, but will output up to 120 watts per channel). It will not have the slam/punch as the Parasound/Hegel. This includes a phono preamp.
Marantz PM-14S1 Integrated Stereo Amplifier-Gold USED - £1,799.00 / $2,363 USD. The Marants is voiced to be warm sounding, warm rich. People love the musicality of it. The jazz type music does very well on all types of equipment, but since you do like to listen to hip hop / rock / R&B, the Marantz will probably not be fast enough for the punch/slam you want (it will be slower and more laid back). This includes a phono preamp.
Buying an external phono preamp (such as PS Audio Nuwave) or an external DAC (Gustard/LKS) will always sound better than what is included in these integrated amplifiers. It all depends on your budget. I would probably lean towards an external DAC because the ability for a DAC to generate a more “analog” sound requires much better equipment. The DAC included in the Parasound is okay, but nothing extraordinary.
I can give you a starting points for speakers (listed on Ebay UK):
New... Monitor Audio Silver 10 3 way 250w floorstanding speakers in Black Oak NEW - £1,150.00 / $1,510 USD. The Monitor Audio has been known to be a very clean sounding and detailed speaker. This one has two 8” woofers which will give you good bass punch (as long as you have enough amplifier power). The C-CAM tweeter is based on ceramic and is very nice. If you look at other Monitor Audio speakers, it’s important to know that the ribbon type tweeters can sound more laid back (which may not be what you want if you listen to hip-hop / R&B).
Cables are a whole new conversation. Lol. The opinions will always be all over the board, but in my experience solid-core conductors always win in my tests. I would avoid anything silver (my own opinion), but rhodium plated are excellent. If it were me and I was starting out, I would look at the best Audioquest interconnects that still have gold-plated RCA plugs (avoid silver-plated in general). The Wire World cables that have copper conductors and silver-clad RCA plugs are also very excellent (such as Eclipse 7).