No you can't game on $300, even for low settings, and expect '30 FPS or more'. You need to spend at the bare minimum of $500 IF you have a LEGAL 'off the shelf' copy of Windows, else your looking at least $600 to around $700 to 'game' in PCs. If your really can't afford (even with a job) that money, then I would suggest staying to consoles as they are MUCH easier to maintain (there is ALOT of work you will need to CONSTANTLY do to the PC).
Mind you this is in ALPHA, meaning it may not even 'play', it isn't completed, it isn't working, expect it to crash or not even work with your system.
That said the cheapest route I seen is head to Walmart, pick up a i5Core $349 PC (8GB DDR3, 500+GB HDD, DVD, keyboard, mouse, Windows pre-install, all under warranty), swap the PSU (600W around $90), and put the rest into the video card ($149-$499) and you got a system usually capable of 1080p 50FPS on High for BF4. Some have used PickParts here and done just as well, but your ON YOUR OWN installing everything (CPU, Fans, wiring, etc.).