I am a HUGE fan of Amazon and recently contemplated some of the same questions.
I have pretty limited speaker mount options so I needed something small. I had a few requirements, small/compact size, an upgrade in sound quality from my Polk RM6750 from 2005 and a tiny center channel since that was my biggest obstacle.
I finally settled on the Energy RC-Micro's because the center channel was so small and had a keyhole mount on the back. This meant I could mount it flush against the wall (much like the Take Classics.)
I've been a Polk fan for years but decided to switch to Energy because I found the Energy speakers seemed to be much "brighter" and generally added a lot more clarity with movies and a lot of different genres of music. The specs on the Take Classic appeared to be slightly better better than the RC-Micro in that the center/satellite channels go down to 110/115Hz as opposed to the 150Hz on the RC-Micro. However, the RC-Micro has been reported to have better build quality and uses nicer materials (per Energy).
As for Polk's system, the only package I'd consider in the compact range is their new Blackstone series. They have a TL1, TL2 and (soon to be released) TL3. The TL1 isn't quite up to par with the other systems you've mentioned above. The TL2 is going to be right in line with the KEF C series and Energy Take Classic and RC-Micro. The TL3 will be the biggest advancement yet in the small speaker world and uses the same technology their high speakers have (ring radiator.) Unfortunately, the TL3 won't be released until late February and according to the Polk rep, the initial MSRP for a package is going to run about $750 (without a sub.)
I can appreciate what you're going through here as I went through the same thing a few weeks ago. But ultimately, most of the packages mentioned here are VERY close in specs, quality and sound. Ultimately this means only you can make the decision as to which works best for you. If I was choosing between a Polk TL2 and an Energy Take Classic, I'd pick the Energy. The Polk's always have (in my opinion) a nice rich and warm sound which is great for music, but just lack a bit of clarity when it comes to TV, Movies and anything with dialogue. I think the Energy just fits more situations. That being said, Polk is a great brand and I wouldn't think twice about getting a set. It really comes down to your personal preference. Given your room size you may even want to consider the Energy RC-Micro. They are just bigger than a baseball, in a nice piano black finish and look great mounted around the room. A very sleek look with my new Sony 55NX810.
As for the free Polk subwoofer. I wouldn't even let a weak sub be a determining decision. Your AVR has an option for 2 subwoofers and (in my opinion), 2 weak subwoofers that are properly placed at WAY better than one great subwoofer. So regardless of what you choose, I'd think about dropping another $100-$300 and adding another sub placed elsewhere in the room. You will notice a huge improvement in how well blended the sound is in the system.
I'd probably choose the following.
#1: Polk Audio Blackstone TL3 - MSRP $749 w/out sub, Not for sale yet - Not available now and really $ but is the best option in this "range".
Tied for #2: Energy RC-Micro - MSRP - $999, On sale for $399 from Crutchfield.com - Lots of clarity and big sound in a little package.
Tied for #2: Energy Take Classic - MSRP $599, On sale for $399 from Amazon.com - Slightly better specs in the center channel from the RC-Micro's but apparently the build-quality is just below the RC-Micro. I'd call it a dead-heat with these two, both being awesome systems!
#3: Polk Audio TL2 - MSRP $499 w/out sub, On sale for $499 and includes a free PSW111 from Amazon.com. In my opinion, the sound quality is probably better for music (depending on genre) than the Energy's, but Polk's compact speakers tend to get a little "muddy" with dialogue in movies and such.
#4: KEF C Series - MSRP $1,149, On sale for $1,067 from Amazon.com. Although I think these are awesome, that price tag is just too big to make them competitive with these options.