I'd want to keep the LCR from similar range, it doesn't look like Fyne have matching F303 center? Also doesn't have the coaxial design from the higher F500 range.
You don't have to buy the matching Fyne sub, other brands like SVS, Rel, BK, Arendel will work ok
I'd recommend higher quality standmounts over lower range floorstanders. I use floorstanders for my cinema and hifi system, but both were bought second hand, and each ones are the flagship speaker in the range, not the low end Kef Cresta etc models- good floorstanders aren't cheap.
There are pros and cons of both designs but at your buget stick to standmounts. Also if you're stepping up range in speakers look at higher model AVR, the lower end Denons have the lower quality room correction, ideally want the full resolution model as it has more filters, more accurate etc.
Have a demo of a few AVR models as well as they offer different sound signature. If the Fyne speakers are bit forward, then you don't want a forward sounding amplifier. When you go and have a demo listen to music, you want a system that is pleasant to listen to for a long time. The "grab your attention" type presentation might be ok for 20 minutes but can be harder on the ears for longer listening. Have a listen to Wharfedale and Q Acoustics to get an ideal what a warmer/neautral sounding speaker is. Then listen to pair of cheaper Klipsch, those are bright and very forward. There are opposites, and if this is your proper system you need to get an idea what you like, rather than buying the first system you listen. It's another matter if you buy a budget second hand system from gumtree, be ok with that for 12 months whilst going around hifi shops/shows, learn the hobby, maybe buy another brand of speakers for a garage, upgrade and change bits over the years, understand differences between horizontal and vertical biamping, high pass filters etc etc.