Thanks.... I am going to shoot mostly moving trains with it, and maybe some child photos, I notice that you are talking the model III my model is the model II, what is the difference between the two???
The II, III, etc, of the 75-300 is only $70~80 commonly for a reason. You didn't get a deal. Sorry to break it to you like that. But you basically bought it at it's going price. It's basically the most budget telephoto lens Canon has made. It's functional, but it's by no means a good lens.
For $30 more, you can get a refurb 55-250 STM which is literally several orders of magnitude better in every single way. You can get it for very inexpensive from Canon themselves, on their Refurb Sales site. With warranty. I would suggest you get this instead.