CPU: I'd go with an i5-3XXX if you need to budget. (figure $180-ish). Pretty much whichever one you can afford, but try to go above the standard 3.0 GHz if you can.
An i7 would be preferable for extensive media work. More-so for things like 3D modeling, but I'm sure a quad-core would help a lot with Sony Vegas, too. The i7-4XXX line runs about $300, but they're definitely worth it if you can afford it.
CPU Cooler: Unless you're planning on over-clocking, you don't need an aftermarket cooler. It'll come with a sufficient one.
However, I do suggest buying better thermal paste than what it comes with. It's a cheap addition that's well-worth picking up,
and I recommend using Arctic Silver.
Memory: As previously suggested, 8GB of RAM would be a nice number to go with. I like G.Skill Ripjaws and Corsair. I like Corsair for everything. =p
Try to aim for a low Cas Latency - 7 or 9 are your magic numbers. Also don't go above 1.5 Volts. Make sure the pins match the mobo (as explained on the mobo)
Beyond that, don't worry too much about the other numbers. The difference in speed between a 1333 and 2400 is negligible.
Storage: Also agreeing with having a SSD and a HDD. Solid States load ridiculously fast. Do bear in mind, don't defragment it. Just don't.
If you can't afford both storage pieces,
Seagate makes a decent budget Hybrid that's worth looking into. Boyfriend has it - I don't like that it doesn't show the partitions of the two different drives... but it works as intended. It automatically stores your OS in the 8GB of SSD so that loads quickly, but then there's no room for much else. So
if you can afford to get both separately, I'd do that. Especially with media work.
Video Card: If you intend on expanding your gaming collection to newer games over the next couple years, I'd suggest looking into at least GTX 650-680 line or so, with 2 GB of VRAM. Mine is a 670 with 4GB of VRAM, so I have yet to encounter any real issues on newer games. Boyfriend got a GTX 760 with 2 GB of VRAM, and he's got no issues for awhile, either.. though you can't account for poor optimization. ;)
However, if you're not, then something cheaper in that line with just 1GB of VRAM would be fine for Sony Vegas and your games, as I mentioned before.
Just don't go with an X40. Gaming ones generally start at X50, like the 550, 650, etc.
Case: Personally, I love Antec and Cooler Master. I have a Haf-X, but those are big and expensive, and not everyone likes really big cases. Though, whichever you go with, make sure it has enough 5.25" bays in the front for your DVD drive(s). Boyfriend didn't account for that, and his doesn't have any external bays - made installing Windows a bigger pain than it needed to be, lol.
Power Supply: I always overshoot, just in case I expand at all later.
I have a 750W Corsair Gold.. I think 750. Anyway, for the parts above, I'd go with a 700-750, and no lower than a 600. Basically, you can overshoot it all you want,
but go too low and it'll fry things you don't want fried.
There's usually only about a $10-20 difference between every 50watts, so I just go up a little bit from the suggested wattage until it feels 'safe.'
Optical Drive: Any good old ASUS drive. They're like $20. Just be sure to have a SATA cable, they don't always come with one. Mine didn't. I bought some really neat blue UV cables to differ my 3 storage drives from the red ones for my 2 disc drives.
If you need any, Monoprice will be your best friend for really cheap cables.
Motherboard I've saved for last. Basically just make sure it has all the right ports, and read the reviews. I went with an ASUS Sabertooth line; it had everything I needed, the whole thing is basically a heatsink, and the BIOS is easy-peasy for pretty much anyone to use. I adore it. c:
If your CPU is an LGA 1150, search for those first.
If you're going on the recommendations for 2 storage drives (a 120~GB SSD and a 1-2 TB HDD) and your 1 or 2 disc drives, then make sure it has enough of the right kind of SATA ports for everything you're installing now, and for possible expansions. Storage drives are usually SATA 3 (6GB/s), and dvd drives are usually SATA 2 (3GB/s), but 3 is backward compatible so aim for more of those.
With only 8GB of RAM, that shouldn't be an issue on capacity, but make sure the pins on the RAM match the mobo's. 240-pin is pretty much the standard for both, but always be sure.
Power Supply also comes in here. It might need to be a 24-pin, might need a 20-pin. Many these days, like the one I linked, are 20+4 so they would go in 20-pin mobos or 24-pin mobos.