To get the most from other people's games, it makes sense to look at games that were played well. However, what a beginner needs to see is not perfection, but what happens if one player makes a mistake, and how the other player punishes it. This means either looking at games where only one of the players is a master, or at games played by two masters that were annotated by a master to show what would have happened if certain bad moves had been played.
There are quite a few good ways to do this. The most economical use of time is not to watch a live game, because this involves long delays, interruptions, and incomplete and erratic delivery of any offered analysis.
Instead, the most economical use of study time on master games is to replay a game that has annotations, ideally accompanied by explanations in English (or some other language comprehensible to the reader). Perhaps the best idea is to find classic games by one of the masters in the Romantic Age of chess that are comprehensively annotated, but almost any master's game should yield benefits.
A word about annotations: Many games are annotated by masters for masters. Examples are those analyses that are published in Sahovksi Informator ("Chess Informant"). These contain no words; all games are annotated with only variations and glyphs representing chess concepts, ideas and evaluation results. They would be incomprehensible to a beginner. What I'm referring to are games like those annotated in USCF's Chess Life, or the collected games of a master such as:
- "My 60 Memorable Games", Bobby Fischer
- "Fire on Board", Alexei Shirov
- "The Sorcerer's Apprentice", David Bronstein
- "I Play Against the Pieces", Svetozar Gligoric
- "The Life and Games of Mikhail Tal", Mikhail Tal
- "Alekhine's Best Games: 1908-1923", Alexander Alekhine
- "Alekhine's Best Games: 1924-1937", Alexander Alekhine
- "100 Selected Games", Mikhail Botvinnik
- "My Best Games of Chess", Valeri Smyslov
- "Capablanca's 100 Best Games of Chess", Harry Golombek
Another source is Everyman Publishing's "Move by Move Series". I would recommend the books in this series on Paul Morphy, Victor Korchnoi, Raul Capablanca, Mikhail Tal, or William Steinitz. They have the advantage of being published in e-book format.
"The Amateur's Mind", by Jeremy Silman, approached this technique differently with the (relatively) novel idea of looking at amateur games, pointing out their flaws, why they were flaws, and what would have worked better.
The other disadvantage of this book is that you won't see an illustration of how to play well, you will only see some illustrations of how to play badly.
That said, since the mistakes made by the players involved are common among amateurs, you may realize that you are also making them, and be able to fix them. Another benefit is that the book tries to delve into why these amateurs made these particular mistakes; the author tries (though a bit unsystematically) to get to the root cause. This may be very illuminating for other amateurs out there.
One final note on Silman's book: Not everyone likes Silman's writing style, which some find abrasive at times, so I recommend that you look over samples of the content in a bookstore, or at your library or chess club. (Somewhat mysteriously, Amazon doesn't seem to offer a preview of this book, as they do with many others...).