To start off, it kind of depends on whether you plan to run a TV and a projector in the room, or if it's just a projector.
For the two options, you're really looking for an AV receiver with dual outputs. One will take care of the TV and do all the fancy ARC audio support so you can use smart apps on the TV and get sound in surround. The second HDMI output is a picture only signal to a projector. The clever bit is that the amp can work out that it's dealing with say two different display devices (say 4K for the TV, 1080p for the projector, or differences in what they'll do with other picture or sound related functions) and keep either one working happily despite the presence of a second display. You can't always guarantee that with a simple 1 in:2 out HDMI splitter, and you probably won't find a splitter that accommodates ARC. Straight away then, you're going to looking at new AV receivers at £300+.
As for the rest of the features, most AV receivers do the same basic functions. You've got audio switching and decoding, network features, app control is pretty standard now, as is some form of streaming from mobile devices whether that's via Bluetooth, or a network connection, or both. Denon and Yamaha both have their in-house versions of a wireless multi-room system.
Once you've knocked out the single-HDMI-output receivers, then most of what you'll find will be ATMOS-capable receivers. It's up to you whether you buy speakers for all the 7 satellite channels that you'll use in a 5.1.2 configuration. You may just decide to run in 5.1 mode, and if you do, you'll get a little more power to each channel since it's only being divided 5 ways rather than 7.
Speaking of power, forget the manufacturer's claims. It's mostly smoke and mirrors becuause the figures are manipulated by crafty ways of measuring and misleading ways of representing the data. A useful rule of thumb is to take the mains power consumption, then knock off 10% for heat loss and the overheads of running the amp, then divide the result by the number of channels that can be actively driven. The Denon AVRX2400h (£299-£349) eats 500W max from the mains. Take off 10% leaves 450W. Divide by 7 gives 64W per channel. Sony claims that its £430 STR-DN1080 consumes 240W. Do the same maths and the figure works out at 31W per channel, yet Sony claim they have the most powerful receiver in its class. Are Sony pulling a VW to keep the Eurocrats happy?
Outright power alone shouldn't be the only measure as to which to buy. You might have your own brand preference, or perhaps certain features might be an essential for you. Denons get good press, as do Yamaha and the Sony. Personally, I like the Yamahas for their ability with music as much as movies.
The ball then is back in your court. Do you need dual outputs, do you need ATMOS, do you need 4K upscaling and analogue cross conversion?
