General tips and statistics.
For the top half, the 35pt bonus is really important. To earn that, you need at least 3 of a kind for 1 through 6, for a total of 63.
For the bottom half, Three/Four of a Kind and Chance, you want to score better than the average of 5 dice, which is anything over 17 total.
As for the Full House and Straights, fish for those early and use the failed attempts to fill in your top half.
For serious players, there is an online application that allows you to compare your moves with those of a computer playing optimally (i.e. making plays that are most likely to score you the highest overall, in the largest number of possible scenarios). Try using it and see if you can improve your thinking.
Another app on that same website lets you play through an entire game of Yahtzee and get all of it analyzed afterwards. Here are the instructions on how to read the analysis.
The game of Yahtzee will challenge the player to choose between chasing similar dice to score the grand prize ( ‘Yahtzee’ is ‘five-of-a-kind’ ) versus a straight where any duplicates are re-rolled to chase the straight. To get Yahtzee means you’ll always need to chase duplicate dice at the expense of a straight. This ‘Yahtzee 1st and foremost’ strategy dictates that you only chase a straight when you get an inside straight (four die, 2,3,4,5) on your initial roll, otherwise you re-roll any dice not duplicated to score a ‘Yahtzee’.
The Yahtzee variant ‘Yams’ introduces an alternative scoring sheet with a few changes. For instance it drops the ‘chance’, ‘three-a-kind', and adds a ‘Rigole’ which is four-of-a-kind plus one from the opposite die face (1 for sixes, 2 for fives, 3 for fours, etc).