$300 is a pretty tight budget. Any more would surely help.
Unfortunately, you are going at this the wrong way.
1. The PSU. A quality PSU from a reputable maker is a MUST. However, the PSU should be the LAST thing you buy, not the first. This is because you cannot properly size a PSU until you know the power consumption of the other major components (CPU and GPU, for example). And while TT is known to make some good stuff, that PSU is not one of them. It only has a 72% efficiency specification, which is frankly, pretty lousy. The better supplies are 80% or better.
2a. Video card and RAM "from friends". That's fine, assuming everything is legal - BUT you cannot take any old RAM or graphics card and assume your motherboard will support them - especially the RAM. If your friends will help you out with extra parts, you need the exact part and model numbers NOW - then find a motherboard that is compatible. That may not be easy.
Note that almost all motherboards have their own webpage at their maker's site. And almost all have QVLs - qualified vendors lists that list CPUs and RAM they have tested to be compatible with that board. You need to buy a CPU from the list. There are too many RAM vendors to test all RAM, so you can buy off the list, but the RAM still MUST have the EXACT SAME specs as RAM on the list.
2b. Since on such a tight budget, consider a µATX board with integrated graphics and Intel i3 or AMD equivalent with integrated graphics support. These too are quality graphics solutions, capable is fitting into $20,000+ home theater systems, and even provide good game "play" - with sufficient RAM and CPU (though graphics affects may be toggled down, and less stunning). An i5 would be nicer, but they cost more too. You can always add a graphics card later, when budget permits (but consider this when selecting a PSU or you may have to buy another PSU when upgrading the graphics).
3. Sound card - Almost all motherboards have "quality" on-board sound designed to be incorporated into home theater systems. Unless you will be doing sound mixing and recording through a midi or the like, you don't need a sound card.
4. Cooling - Understand that both Intel and AMD sell and package their CPUs with a cooling solution - as a "unit". As such, they are expected to be used together. Consequently the use of aftermarket, 3rd party cooling solutions violates the terms of the warranty! Neither AMD or Intel want to replace the CPU or heatsink fan assembly during the 3-year warranty period so they provide excellent coolers!
5. Windows - Understand that ONLY full "retail" licenses for Windows are transferable to another computer. OEM/System Builders licenses that was purchased with, or was purchased for another computer CANNOT be transfered to another computer legally. And of course, 1 license can only be installed on 1 computer. I note this can be confusing when, for example, Microsoft includes a 32-bit and a 64-bit version disk in the same box - but the "license" is for only one.
You need to determine exactly what parts you bring to the table, then determine their compatibility and go from there. I note if these are obsolete or phased out parts, they may force you to buy hardware that will limit your upgrade options during the next couple years.