Your power supply should be fine. With a Core i5 processor and GTX 650 Ti the system will only need about 300-350W, factoring in overclocking.

Everything in your wishlist is compatible, but go with this Corsair memory

I still highly recommend one of the cases I recommended. The Xclio case is nice, but it doesn't come with any fans (as a cost cutting measure). So if you need fans you're going to spend an extra $10-15, plus the shipping cost is higher.

ZALMAN CNPS5X Performa
Cooler Master Hyper 212 Plus

Those are a couple of heatsink options.

Trying to find a better and cheaper motherboard will be difficult. If you take advantage of this combo deal, you can get the i5 3570K and the MSI G45 board for less than the 2500K and G41 board:
http://www.newegg.ca/Product/ComboDealDetails.aspx?ItemList=Combo.1177083

Even though you don't want to change the case, here are some options you should consider because you'll save a good chunk and they are decent cases.

http://www.newegg.ca/Product/Product.aspx?Item=N82E16811147060
http://www.newegg.ca/Product/Product.aspx?Item=N82E16811119256
http://www.newegg.ca/Product/Product.aspx?Item=N82E16811815014
http://www.newegg.ca/Product/Product.aspx?Item=N82E16811124151
http://www.newegg.ca/Product/Product.aspx?Item=N82E16811133094

You can't overclock a Core i3 processors. Their multiplier is locked. You can overclock the bus a very small amount, but it's not recommended and you'd only get at most a couple hundred MHz. The reason you would want to get a Core i3 processor now is that, at stock, they do compare to AMD quad core processors in performance but you have the option of upgrading to a superior i5 or i7 processor later.

If you go with an AMD processor they do require a better power supply when overclocked. They'll use up to, and sometimes greater than, 100W more than an Intel chip when overclocked. So with the video card you chose, you need a name brand 400W power supply minimum. A no-name 4-500W won't cut it for overclocking.

Now with that said, you can shave off a few bucks from your original build and just get the cheaper Core i5 3450. It has a limited multiplier to allow some overclocking, but its performance is still very good at stock to get you smooth framerates in TF2. And FYI don't forget to look at combo deals. The 3450 has discounts when bundled with certain motherboards and there are a couple of cheap alternatives that you might be interested in:

http://www.newegg.ca/Product/ProductCombos.aspx?Item=N82E16819116506&SubCategory=343&fromcs=0&bcmTag=0&SortField=0&PageSize=100&Page=1

If you can't get an i5, your next best option would be the AMD FX-6300 (Vishera). And if you can't afford that then get the AMD Phenom 965.

Since you plan to overclock with the AMD chip you will most likely end up spending a bit more for a robust motherboard. Once you find a motherboard you like, cross reference it with this list to make sure it'll handle overclocking. I'd recommend either of these for your budget:
http://www.newegg.ca/Product/Product.aspx?Item=N82E16813131873
http://www.newegg.ca/Product/Product.aspx?Item=N82E16813128519

Lastly you should swap out that RAM for a different model. Those heatspreaders on it are big and could potentially interfere with an aftermarket CPU cooler - depending on what heatsink you choose to get. Corsair offers alternatives.

If you want to get a Core i5, for under $500, you'll have to basically change everything, including the case, and get a much weaker video card.. If you are willing to swap out the case and keep the 650 Ti, you can build an AMD (or Core i3) system for just under $500.

Options from newegg.

http://www.newegg.com/Product/Product.aspx?Item=N82E16883258007
http://www.newegg.com/Product/Product.aspx?Item=N82E16883227444
http://www.newegg.com/Product/Product.aspx?Item=N82E16883227436
http://www.newegg.com/Product/Product.aspx?Item=N82E16883227457
http://www.newegg.com/Product/Product.aspx?Item=N82E16883227443

http://www.tigerdirect.com/applications/SearchTools/item-details.asp?EdpNo=4990118&CatId=1886

http://www.tigerdirect.com/applications/SearchTools/item-details.asp?EdpNo=4959026&CatId=1887

http://www.tigerdirect.com/applications/SearchTools/item-details.asp?EdpNo=4990119&CatId=1886

Those are better options from tigerdirect.

That's ok, but you can do better.

Are you against building one yourself?
What games, specifically, do you want to play?

Building one yourself means you get more flexibility. Those prebuilt cyberpower PCs will give you the cheapest motherboard and power supply they possibly can. By building one yourself, you can choose your own power supply and motherboard and keep upgrade options in the future in mind.

You can turn up texture quality (mat_picmip), anti-aliasing, anisotropic filtering, and screen resolution. For everything else you'll simply want to use trial and error to see if the IQ gained is worth the performance lost.

A better GPU wouldn't help TF2 performance when streaming. When not streaming there could potentially see a boost, but we're talking about something along the lines of going from 170 frames to 200 frames. The GTX 280 should have no problems running TF2 over 100 fps on high settings, and a lot more frames if using custom configs. The only way to burden the GTX 280 would be to use above-HD resolutions and/or high levels of anti-aliasing (16x, 32x, super sampling).

TF2 and streaming are processor intensive. The CPU will be taxed before the GTX 280 will be. Andthe 280 is no slouch of a card for DX9 games. The biggest boost from a video card upgrade would be in DX11 games.

The OP reformatted and his performance is better now. It was most likely a driver problem.

Streaming doesn't affect the video card at all. The video capture is done on the CPU.

Apparently 120 Hz LCDs can be CRT-like.

http://marky.com/backlight/lightboost-zero-motion-blur/

If you get a Phenom II X6 processor, which your board supports, when streaming you should get similar framerates to what you get now. The x6 processors aren't really sold in retail anymore, but you can easily find them used. Compared to your current processor an X6 would be a decent upgrade. You get L3 cache on the chip, which Athlon IIs lack, as well as two extra CPU cores. You would see a small bump in TF2 framerates when not streaming, but nothing drastic. If you want a lot more performance you simply need to upgrade to Intel.

Do a clean install of the drivers.

*When you take the evidence public.

Depends on the make/model of the PSU. Some 550W are garbage and some are really good.

But after 5 years it wouldn't be a bad idea to upgrade it.

What time do you play?