PSUs follow a common formfactor. There's some variation in depth but the height, width, and mounting screw positions are specified by the ATX12v 2.x formfactor to which they all conform. You should be able to replace that 300 watt PSU with a 500 watt one quite easily. PSUs that are rated at 1,000 watts or more may be a bit deeper, but should still fit.
One thing that you will have to be wary of is the airflow. Some PSUs have the air intake on the bottom, while others have it on the rear. Some cases may secure the PSU in a way that blocks airflow to the bottom of the PSU so be careful of this.
As for PSU brand, Sea Sonic is the best but also demands a price premium. Enermax is another reputable manufacturer which is a bit more affordable than Sea Sonic. Corsair, Antec, and XFX don't manufacture their own PSUs but only source them from reputable OEMs such as SeaSonic, Enermax, Delta, Flextronics, and CWT. Any of those listed brand names will do you well.
Other rebranders such as OCZ, Thermaltake, Cooler Master and Kingwin are all over the place.