What's the best game and the easiest game for a rookie gambler to play at when at a casino and why?

Before answering your question directly it is important for you to understand that casinos make money by always having the odds in favor of the casino. Consequently you cannot ever expect to become a professional gambler at a casino unless you play a game where you take money from other players instead of the casino. That means playing poker, and playing it better than other players at the table.

The answer by "Divide By Zero" is correct that the easiest game to play is slot machines.

The answer by "Tasm" correctly identified the games that have the lowest house advantage, which means that you will lose money less quickly most of the time by playing those games.

The slots, it's a no brainer.

Blackjack with good rules that favor the bettor.  You can use a strategy card, they sell them in the casino gift shop.  Combine that with a good progressive betting strategy.

Craps:  come, pass, don'ts, place bets on 6 and 6, no prop bets and again a good progressing betting strategy.

Roulette; 1:1 bets

Baccarat.

Even with perfect play, all the above have a house edge.

Now just play poker.  I'm playing against other people and have done pretty well.  The house makes their money on the rake.

Blackjack I guess.

Penny Keno, you will lose barely anything and canplay all day. 

The roulette wheel, betting

black and red or odd and even.

Blackjack is considered to be the easiest game to learn and win because it's fairly basic and easier to predict odds via card counting.

The easiest to play is slots. Why, because it requires absolutely zero brain activity, in fact it's something a baby could play, or even a cat. (How this is useful info for someone trying to become a professional gambler, I have no idea. You've got until May 4 to ask some good questions. Good luck!)

          Baccarat has your best chances. It is easy to learn too. Some people might say blackjack, but you have to memorize the plays to have any chance. Another thing people say is to play the pass line at craps, just the pass line.