Hi and welcome.
Never buy a cheap and nasty power supply they can go wrong and take out all you other expensive components at the same time. Not only that just because it is marked 600W often they are nowhere near that rating. Purchase a good make like Seasonic, CWT, Corsair, Thermaltake, Enermax, Gigabyte, Coolermaster, Antec, etc and try and get one with a single 12V rail if possible. I would advise you to get one of about 650W minimum depending on your hardware demands.
Once you have a decent PSU running your system you might well find that the problems disappear but if not at least you have a good base to start from. It is the foundations of the computer after all.