I can't quite visualise your wall design. It sounds like you're describing some kind of brick plinth @ 18" deep x 20" high on which an 8" deep false wall will sit. Is that right?
In the meantime, here's some basic info on speaker principles that might help you narrow down your choices: Most box-type loudspeakers work best with some space around them, even bookshelf speakers. Enclosing them within a built structure means you'll hear a difference in the sound. With some designs it's more pronounced, and with others less so, but they all change in character to some degree. Speakers that change the least are sealed box designs, but unless we're talking about the sort of micro-cubes made popular by the likes of Bose, then conventional bookshelf/standmount speakers in a sealed box design have been out of fashion for a good 30+ years or so, so this leaves ported designs as your main option.
Broadly speaking, ported designs have the bass port either at the front or the rear, and since you'll be listening to the sound of the port as well as the main drivers, then clearly you need to limit your choices to front-ported designs. You'll also need something where the manufacturer offers centre speakers as well. As a practical consideration, it'll probably simplify construction and fitting if the speakers have flat sides rather than being tapered or curved or with lumps a la KEF Q1 or similar.
This brings us to a limit within your wall design; it's the depth. Front ported speakers that match the rest of the requirements for porting and performance and shape do tend to be a bit bigger than the smallest rear-ported bookshelf speakers. The larger facia required to accommodate a bass port generally goes hand in hand with a deeper box too. In short, an 8" wall depth is going to limit your speakers choices.
The most compact ported speaker I can think of with a range of matching centres that fits your budget and performs well above its price point is the
Wharfedale 220. Including the speaker terminals, you're looking at a depth of about 10.5 inches.
Wharfedale Diamond 220 had an original price of £220 when launched in 2014. The got a lot of praise and won awards at that price. They're currently on offer for around the £100 mark which makes them something of a bargain. Used prices reflect the higher RRP. Ebay shows a lot in private sales for around £70, with the odd pair dipping in below £50. Potentially that would then leave you with up to £200 to spend on a centre speaker. For a movie system, the center speaker should take the lion's share of the front three speaker budget. Most of what you hear during a film comes from the center.
As for small but high-performing subs,
@hornetstinger is right that that combination means something expensive. Many years ago, Bob Carver's Sunfire True Subwoofers broke the big box rule. He found high-quality long-throw drivers to mate with potent amps and created small boxes that did stuff that surprised the big box market at the time. The same sort of principle has been applied widely by other manufacturers now. Back in the early 2000s REL made the Q200 sub. It's a 1 cu ft box with a 10" driver, so on paper it looks the same as a BK Gemini II, but in the flesh it sounds like a much bigger box thanks to the additional power and the quality of the amp and driver. These were £600 new. They're not the prettiest sub, but if you want potent performance from a tiny box then they're really hard to beat. You can pick them up used for under £150.
