300w with a dedicated GPU is really pushing it, but there is more to the PSU than just the 300W figure.
Can you provide an image of the sticker on the PSU? What is the brand, specifically?
It may say 300W, but there will be a maximum wattage on the 12V rail, for example, with a maximum Amperage, this is important, because a higher spec GPU will need 30A/35A or higher..and if your PSU provides, say 250W at only 24A, then you will run into stability issues.
Ideally you only want to use up about 70%-80% of your total Wattage, never pushing the PSU to the max, unless it's a good quality one (like an "80+ Gold" certificate).
I don't have the link, but on this website, TomsHardware did a rating/chart for loads of PSUs, worth searching for (maybe another person can assist with the link?).
Any upgrade on Hardware design (Sandy/Ivy Bridge, Kaby Lake, etc), will provide an improvement in performance, when doing a direct comparison, but this really depends on the GPU.... between the i5 & i7, performance will be fine on either, it's the GPU nowadays that does most the work.
You can definitely improve you performance with RAM, 1600Mhz DDR3, with 8Gb minimum (for a 64bit system) is the minimum respectable RAM nowadays.
But going for Ivy Bridge, maybe some 2133Mhz DDR3, or straight DDR4, and last but most certainly not least, an upgraded PSU will definitely help!
Waiting for your PSU's exact specs/model No.