As you can see, there are a lot of options available. If you are open to getting new speakers, note that most of us on the forums tend to lean towards neutral speakers with a flat response as that tends to yield the most realistic sound reproduction. Better to get a flat sounding speaker and use EQ than to get a speaker that is bright or bottom heavy.
Two well placed speakers can produce a phantom centre image if you sit in the centre sweet spot for listening. You can try a staged approach. Try 2 speakers alone, and if your really feel you need the centre channel, you can add it later, unless you are set on having a centre channel now.
Unless you go with something like the LS60 above. There is no matching centre for those speakers and no option to add surround speakers later. They are strictly for 2 channel listening. You would not need the Yamaha as they are powered speakers. You connect your devices, like your TV and any music sources, to one speaker and the other speaker receives the audio wirelessly. It is a nice compact system for 2 channel listening.
If you want the centre channel and the option to add surround speakers, stick with the Yamaha. In your price range there are some great speakers. The HT Towers and matching HT Center from Philharmonic Audio are very neutral speakers and I've listened to some of their speakers in the designer's home in Maryland. They have a beautiful finish and would be a top contender for me. They produce them in batches so you have to wait for stock as they sell quickly. I would email them about current wait times. They sell direct but they have a good community of supporters. If you want to hear them, someone in your area could be willing to let you have a listen. The BMR monitor, BMR Tower and HT Tower have a similar sound to each other.
Arendal also make a great speaker and you can try in home with free return shipping if you don't like them. They are quite heavy, though, but that might be incentive to keep them rather than box them up again.

They get great reviews and like the HT Tower have good bass extension and likely would not need a subwoofer unless you want the low frequency effects from movies and TV.
A lot of stores carry KEF and besides the LS60 you could consider the R7 Meta or R11 Meta. I would also second the mention for the Mofi Sourcepoint. Very well measuring speaker and highly regarded. If you like horns, the JBL HDI-3800 is another option. I have listened to the 3600 and they are a nice sounding speaker for the money. The 3800 received a very favourable review on Audioholics.
The KEF, Mofi and JBL brands are the most likely options to be found locally if you want to audition the speakers first. In your price range, Focal and Revel are also options that may be available in your area. If you know of some retail shops that are within driving distance, let us know what brands they carry and members here can recommend some models to try and listen to.