Tell a beginner the consolers

Think about buying a PS4 and a simple full HD TV, but with a little searching I stumbled on how the games PS on a monitor of the same laptop using Remote play via an Ethernet cable because it is a little doubtful as to the speed of your Internet thinking about this option, actually the question is: to log in via code generated by the PS will have once or every time you want to play using Remote play? Next question: are there any discounts for buying the PS4 official Sony store in the same new year or other holidays and what you should consider when buying a TV in the first place, is it possible to find a in the range of 10K or less?