I have the 5.1 Energy Take Classic with the sub, and I additionally bought two Energy RC-10's to take the other 2 spots.
I want a receiver that can handle these speakers well, and get the most out of them, while also falling into a pretty tight budget. I'm not too worried about upgrading in the future as much, as I will probably just use this for a long time, and than do a complete overhaul.
You might want to consider the Denon AVR-1913 in your list. There is one on Ebay that is factory refurbished from an authorized Denon dealer with a 1-year warranty that would be well under your max cost figure. It has Audyessey EQ.
Also the Pioneer 1122 new will sell for a price within your range IF you call the dealer, or just check with Newegg and other online dealers that Pioneer has authorized. They use a different EQ, but the reviews are pretty good.
And one to consider is the Pioneer 1120 or 1121. They are older models but have THX certification and they too generally sell used/refurb'd within your budget.
Of these models, note that Audyssey 2EQ cannot EQ the sub whereas MultEQ and MultEQ XT can EQ the sub. On Denon AVRs, MultEQ is the lowest version offered. Give either AVS Sales or Electronics Expo a "call" and see if they have any of last year's models on clearance inside your budget, either 1912 or 2112CI. By calling you can likely even get the newer 2113CI inside your budget.
So you have the Energy Take Classics with RC-10s as fronts? You really need to replace the center speaker, its the weak point of your setup and can't keep up with the RC-10s. You should buy the RC LCR while it is a bargain price at $199.