I'm currently building a new computer on a fairly tight budget. I stole a build from that other thread that I'm using, this, but I basically don't really know how to pick a PSU. My estimated wattage is 255W, does that mean I only need a PSU with that much or is there other stuff I have to consider? Anyway, I'm looking for either suggestions on the cheapest possible PSU that'll support this system without causing it to melt, or just general tips on picking one.

EDIT: I should note that I don't plan on overclocking or anything.

This - http://pcpartpicker.com/part/seasonic-power-supply-s12ii380b

If you're planning an upgrade in the future, then you need to pick PSU which will allow this without a problem. And though it depends on opinion and experience, never take a PSU that has power output lower than "estimated power consumption + 50%".
Judging from some reviews on your CPU and GPU they can easily go over 300W on full load (and it's w/o some power drawn by disk system and such). Going for 500-550W PSU will not be a mistake. Just go for a really good known PSU model. They tend to match their specifications, unlike cheap ones.

In a few words

- always go for a reputable brand (seasonic, corsair). Better pay a bit more than have a fried motherboard/cpu/ram
- consider certified psu's. Psu do lose efficiency over time. Certified psus lose less than others
- always make sure to have some spare capacity. In your case, I would not hesitate to go for a 450 W PSU, as it leaves soma margin for more ram, etc.
- if you consider that you may, in the future, add a middle range GPU, go for a 600W instead

I've built many a computer. Never skimp on the PSU. A poor/weak PSU can cause all sorts of problems and instabilities. The worst part of it being that those issues are often difficult to diagnose when they happen. You can assume that maybe it's the PSU, but you can't really know for certain without buying a replacement and switching it out to see if it fixes the issue. It's the same with motherboards. People are always concerned about spending all of their money on the top video card and processor, but the truth is that you should *always* buy a premium PSU and motherboard.

To answer your question, you definitely want more than 255W. Think more like 450-600W. I've had good experience with Antec, Corsair, CoolerMaster, and Thermaltake.

if you hate psu fan noises or any fan noises, u can get Seasonic SS-520FL2
its review link > techpowerup.com/reviews/Seasonic/SS-520FL/

I´d pick a 450W - 500W range PSU, it´d be enough power for that and would have power to spare even.
Remember that PSUs give less power the hotter they are so as you approach your PSU maximum output, temperature will start to rise due to higher current volume that rises electrical current resistance. So as you approach your PSU maximum as it gets hotter it´ll start to stress it and lower the output.
Now with brand name PSUs that wouldn´t be an issue as they have enough cooling plus they have a good built quality. The important thing though is you said cheap. You could get a cheapest of cheap no name and it will work, though, I wonder for how long and under which circumstances. Now you can go cheap either with a good build quality, which I recommend or you can go cheap with the cheapest of the cheap all other things aside, which personally I would stay away from, not only from a temperature stand point but from a quality point of view, take into account most brand name, even the cheap brand name ones have all sorts of control circuits like overvoltage, peak, low tension and other electrical protections which the cheapest of the cheap no names usually lack.
It´s up to you, but at least you can have an informed purchase ; )

Never pick a cheap PSU, motherboard or processor. You will pay for the choice in the end.

For your PSU look at what you need and add a minimum of 20% for external hard-drives, USB connected equipment, etc. Or better yet 50% for you to upgrade over time, that is the whole point of PC gaming, to upgrade the same rig for many many years.
I personally would go with a ~500W PSU as changing a graphics card alone can drastically increase the amount of power being used, as could adding more RAM or extra hard-drives.

Also if you can try and get a PSU with a silver power rating as for a lot less money then a gold they will still offer a very good and steady power supply even at higher loads. This will enable you to have a fairly efficient gaming computer when everything is running flat out.