The speakers will sound great with any decent receiver. Both the Anthem and Integra are great AVR's. I don't have personal experience with Yamaha, but they have a good reputation and plenty of people are fans of their products. In general, I would advise you not to "overbuy" electronics and focus your available budget on the best speakers you can buy. Pick a receiver that has the features you want and a decent output (keep in mind that, despite what a store owner says, there is very little sonic difference that you will notice in a receiver that outputs 100 watts/channel and one that outputs 125 watts/channel). There are some people (and audio store owners are usually in this group) that will swear that a particular set of speakers "pairs" better with one AVR over another. I think that is crap. The AVR is responsible for translating the audio signal from the source into an electric signal to the speakers - it has no idea whether it is outputting to Viennas or B&W's or whatever. You will get the most audio for your money focusing on great speakers and room treatments. The only other thing to consider is whether you want room correction (Audyssey, Anthem, YPAO on Yamaha, etc.) or not. If you do, the Denon X4000 can be picked up for $1000 or so and has Audyssey XT32 which many people swear by. Others love Anthem's ARC system. If you're not going to use room correction, then it doesnt matter.
Same thing with the Blu-Ray player. If you need something that will handle multi-channel audio (SACD and the like), then you probably need a high-end player like an Oppo or something comparable. If you're just going to watch movies, I'd pick up a Panasonic in the $100-150 range.
One other thing - you haven't mentioned a subwoofer. If you love great audio, I would recommend swapping your speaker choices to some bookshelves and pairing them with a great subwoofer from SVS, Hsu or the like. You can usually get more bang for your buck from bookshelves than towers and the sub will do a better job with the lows than the woofers in the towers anyway.
Good luck!