Translation:I would like to wear those red shoes.
'Me gustaría' is mostly used when you are expressing something that you would like to do.
For example : Me gustaría ir al cine. I would like to go to the movies.
'Quisiera' is used mostly when giving some sort of polite command or indirect order or even asking for permission. As in your example, 'Quisiera reservar una mesa...' You are expressing what you wish to be done for you, in other words, you are somehow giving a command. As opposed to Me gustaría ir al cine where you are simply expressing a wish or desire.
EDIT: And Marktaku1 mentions using "se puso" as a translation of "wore" here, mentioning that it's a natural usage in Mexico.
The robots voice sounded like it said "Hiciera" and I got really confused