You don't actually say what you are trying to do with this lens. That matters.
This is the domain of the bird and wildlife photographers where useful lenses start at 300MM and go out as far as your pocketbook can handle (and then some). It gets expensive fast, and the inexpensive lenses typically have tradeoffs that may strongly impact your ability ot take images or the quality of the results. I've talked about this in some details in terms of bird photography here: http://www.chuqui.com/2013/06/getting-started-in-bird-photography-choose-your-weapons/
Without knowing your expected uses this may be off-base, but let me make some suggestions:
First, be wary about putting teleconverters on zooms. Zooms start off slower than prime lenses(in general) and the teleconverter will soften your image to some degree, and that loss of sharpness is more pronounced on zooms than on primes (again, in general). it's also "one more thing" to carry and attach and detach and it complicates your life in the field.
Adding a 2X teleconverter to any lens slower than F2.8 will cause you to lose Autofocus. Adding a 1.4x TC to any lens slower than F4 will cause you to lose Autofocus. That is likely a serious limitation. On top of that, you'll find manual focus can be challenging because of the loss of light, especially in bad lighting conditions and on lower-end camera bodies like Rebels. (I used to think I was incompetent because I fought manual focus and usually lost. Then I upgraded to a 7d. Sometimes, it's the gear).
Some gear choices I've worked with extensively that worked for me:
Canon 100-400 -- the old venerable warhorse. My guess is this is the lens you ought to buy, and you're looking for alternatives that'll do what it does but for less money. Honestly, I don't think you'll find it. It's the go-to lens for many for a reason. Be wary about buying it used and test it extensively if you do -- make sure you can return it if you get a soft lens. (why? read here: http://www.chuqui.com/2012/09/thoughts-about-the-canon-ef-100-400mm-f4-5-5-6l-is-lens/ )
Canon 100-400 with 1.4xTC: it works, but I found it unacceptably soft.
Canon 100-400 with 2.0xTC: I've done it, but I would argue the images are rarely usable. it gets really soft. That said, I do have a few in my collection that were made with that combo. But I feel it's more luck than skill, and they're soft.
If what you want is a good birding lens (400mm or so), and the zoom isn't as important, the 300F4 +1.4x combo is quite nice. I found it as sharp as the 400 F5.6 and more flexible (becaues you can remove the TC) for about the same price. It's not AS flexible as the 100-400, but it's faster AF and sharper. Love this combo, actually.
My current lens: 70-200 F2.8L IS II (note: not IS, but IS II. HUGE difference) with a 2.0X TC III (again, not TC II. Huge difference). I'll hold this combo up for performance and sharpness against just about anything. Of course, it costs 2X the 100-400, but you're paying for what you get.
Any of the xxx-300 zooms: nice, but it's worth getting the 100-400 instead.
any of the xxx-200 zooms with teleconverter: unless it's that 70-200F2.8L IS II, you'll be disappointed.
Third party lenses. The sigma 50-500 gets raves from some and rants from others. Images I've seen from it are okay, but at the higher ranges, it gets soft. All zooms do, but again, test it before you buy and see if it's sharp enough for you. I didn't see it as an upgrade against the 100-400.
Ultimately, I think most people who are looking at something that goes into the 300-400mm range look at the 100-400, decide it's more money than they want to spend, go look for a cheaper alternative, and either go back to the 100-400 or buy something cheaper and end up regretting it (I know many who did, and ended up with a 100-400). The 100-400 is the best overall lens for someone starting out shooting in this range.
Unless you already own a good 70-200. then go for the 300F4+1.4 combo. Plan to either swap lenses or carry two bodies, though. I did, and that's ultimately why I upgradeded to the Big, Heavy, Expensive 70-200 combo. But don't start with that setup -- seriously. It's way expensive and you will get good results from less expensive gear until you get serious enough to be able to justify a high end lens like that...
(editorial: L glass is definitely worth the cost, but most newer photographers probably can't shoot to take advantage of it reliably. I think anyone who's willing to consider the 50-500 probably shouldn't spend money on L glass yet. but some day, you'll look at an image shot in L glass under a loupe and see why photographers pay for it.. I know I did...)