You can't really go wrong with a Rega amp. The Brio range has been making lovely noises for more than a two and a half decades. In that time it has seen progressive improvements to features, power and creature comforts.
The Brio-R version was launched in 2011. It is fairly new in Hi-Fi amplifier terms and was only superseded last year. That makes the Brio-R a reasonably safe buy for a novice as it's unlikely to have any issues with ageing component's to worry about.
It's going to be tough for you as someone who hasn't heard any half-decent Hi-Fi gear to appreciate when you're listening to something that is exceptional (or even just good) within it's class. If you'll forgive the analogy, it's like being handed the keys to your first car, a Porsche Cayman. That becomes your 'normal' and so you'd never truly experience just how much better that is compared to more mundane motors. So it is with certain pieces of Hi-Fi. If your starting level is way above the mundane then you'll never have experienced that right of passage that is the progression of upgrades from stuff that just makes a noise to stuff that gets your heart pumping, your foot tapping and that makes you want to play tune after tune after tune.
Continuing the car analogy then, the original Brio was the equivalent of the Mazda MX5. It was a joy to use and put huge smiles on peoples faces. Just like the little sports car then, the Brio amp was (and still is) agile, responsive and fun. It set new standards in its class. That made it a bloody hard act to follow for both the competitors and the manufacturer, but also for end users. You see, when an amp does so much right then finding the next upgrade becomes a much harder a task. It's easy to think that spending more will buy better performance. That may be true for power, but isn't the case for what really matters which is enjoyability.
The Brio-R retains the fun of the early 90's original but with the added creature comfort of a remote control. It has enough power (50W/ch in to 8 Ohms, 20Hz-20kHz) to drive good speakers to neighbour-annoying levels, and if you ever wanted to sample the delights of vinyl then it would be hard to choose and amp with a better phono cartridge input.
The 2017 version of the Brio amp is £600 at retail. If I was you I'd look at both this and the Brio-R in the used market. Brio-Rs sell for around £300-£400 used. Anything north of £400 for an -R and I'd be looking at the newer Brio which goes for £400-£500 used.
Your speaker choice is really broad. The larger and better quality speakers in your price range should all be very efficient (90-92dB/W) which means they're good at turning amplifier watts in to room filling sound. Personally I like Focal speakers. When they first came to the UK the brand was called JM Lab. I have JM Lab Electra 905 which I sort of bought by accident
Although they're standmount speakers the internal design (transmission line) and the quality of them means they give a lot of floorstanders a run for their money in the bass department and beat many of them for agility and timing.
I wasn't intending to buy the 905s, and indeed the first few times I saw them at a dealer's place I thought they looked hideous. TBH, with the grilles off I still do. However, I was doing some work for a guy setting up his projector and at the same time I was in the market for some home cinema speakers. I had had a lucky escape on some Dynaudio Contours - the seller buggered about and then withdrew - and so found myself back in the market again. We did a deal and the full Electra 5.1 package he had came home with me. I wasn't intending on keeping them either, but once I had them hooked up to a very nice Tag McLaren processor and a stack of Rotel power amps the Electras really grew on me. I have had them running with all sorts of front end gear from little British 20W/ch Hi-Fi amps through to monster powerhouse Japanese stuff and they've never failed to impress me with their insight and rhythmic timing.
The point of this little ramble is that we don't always appreciate what we have at first. I didn't with the Electras, and it has been the same story in the past with other bits of Hi-Fi. Figuratively speaking, the keys to my first car weren't quite a Porsche Cayman, but they were definitely an MX5.
I've heard better speakers than my Electra 905s, but nothing the south side of £3000/pr that would tempt me to make a change, and even then I think it would be more of a sideways move. It's only with experience that we gain some insight. Coming in as a complete novice it's entirely probable that you'd be blown away by an Onkyo A-9010 amp hooked up to a pair of Monitor Audio Bronze 2 speakers. Add speaker cables and stands and your total spend brand-new would still be under £600. At that point you might even wonder how anything more expensive could ever sound better, but it can. What's a tougher question to answer is whether you'd appreciate the difference.
If it was me then I'd partner the Rega amp with some Focal Chorus 826W if I could find a pair. There are other speakers you could choose. Just try to avoid anything with an aggressive top end or that's bass-lite.
At this point you might be thinking "All I wanted was some recommendations. I thought this would be easy".
It is. Anyone can throw in random recommendations, or even heartfelt recommendations for gear they really love. In the end though it's a question of finding gear that satisfies you musically. Part of that journey is learning what makes "good" sound. That's something where you really need someone experienced to guide you in person. It's not knowledge you get get from reading.
