How to pick a step down transformer for powering MCU?
At the 300mA current level you'll be throwing away a lot of power in the regulator, so I second Chris's suggestion to use a switching power supply wall wart or module.
Anyway, the rule of thumb is that you need a transformer RMS AC rating that is 62% higher than the DC current requirement. So for 300mA you'd need 440mA, call it 500mA or better.
As far as the existence of price differences they often occur due to different distribution schemes and more important issues such as safety agency approvals for various parts of the world. The approvals may be a routine thing, but more likely the unapproved transformer uses materials or techniques that are sub-par. That is also true of switching power supply modules, perhaps to an even greater degree.
Any transformer (or other mains connected device) can create heat and smoke. Keeping it within a grounded metal housing and properly fused will reduce the risk. Commercial AC adapters that omit the fuse and have a plastic enclosure are carefully designed to fail in a relatively benign way (the ones with genuine approval markings are anyway).