Because of the scoring system, Zung Jung encourages players to try to create patterns that score around 30 points. If you go out with a hand that is worth less than 30 points, you are taking a risk because the hands that are worth 30 points can sometimes be completed very quickly, so you could fall behind in the scoring. You are also taking a risk because you might get more points from your hand with just a few more tiles, and you'd leave points on the table. If you go for a hand with more than 30 points, you risk someone else completing their own 30 point hand faster than you. So most of the time, you are going to want to go for a 30 point (or so) hand.
Thankfully, there are only six common patterns that score in this range. In the early stages of each hand, you should be looking at how you can shape your hand into one of these.
10.2 Seven Pairs, 30 points
No hand is ever more than six tiles from ready because of seven pairs. This is pretty straightforward to play: Discard single tiles you hold that you've seen. Throw honor tiles and middle tiles early, as these are more dangerous near the end of the hand. Starting with this hand can also lead us into the next one. This hand is very difficult to defend against because the pairs you keep are not related to each other. Consider going for this if you have three or more pairs. One reason not to claim early exposures is to keep your hand flexible enough to attempt this pattern.
4.1 Four Triplets (all pungs), 30 points
This is another easy hand to try for. Pung anything you can get, especially a dragon for ten extra points. This is also hard to defend against because your triplets do not have to be related to each other unless you are trying for more expensive patterns. Your opponents will see what you are up to, and could fold their hands if you have two or three exposures just so they don't have to pay for your winner. Consider this if you have three or more pairs. Seriously consider this if you have two concealed triplets early in the hand.
2.1.1 One Suit and Honors (Clean Hand or Half Flush), 40 points
In this pattern, you have tiles from only one suit plus honor tiles. The risk in this one comes from claiming tiles. If your first two exposures are 1, 2, 3 dots and 8, 8, 8 dots, the other players will be watching dots very closely. An honor exposure early will help muddy the waters, but this is still tough, warranting the extra points. Consider this if your hand has seven or more tiles in one suit.
6.1 Three Similar Sequences (Mixed Triple Chow, Three Color Run), 35 points
This pattern consists of three chows of the same numbers, one in each suit. This is also easy to detect if you claim discards early on. This pattern often combines with four chows and all simples for 10 more points which is a tidy score. If you have a good mix of tiles, this can sometimes easily change into the next pattern.
7.1 Nine Tile Straight, 40 points
Three chows containing all the tiles in one suit. This one is a little more rare so gives more points. This one can sometimes pair with One Suit and Honors for a serious 80 point hand, so sometimes it's good to be waiting on two tiles in another suit just to throw off the table.
8.1.1 Terminal or Honor in Each Set (Outside Hand), 40 points
This pattern means that every set in your hand must have a 1, a 9, a wind, or a dragon in it, including the pair. This is the hardest pattern of the six to obtain (even though it scores the same as the straight, it's about four times as rare!), and is very obvious to the table if you claim tiles. It is undervalued, and should not normally be tried for unless you only need a few tiles to go out at the start, and should quickly be abandoned if it looks difficult. See if you can move to one of the other easier patterns instead.
These are the six basic patterns you should consider with each hand. Learn them well.
There are four more patterns in this scoring range that are more unusual, but advanced players will keep them in their back pocket.
3.2.1 Small Three Dragons, 40 points - consider if you have two dragon pairs early in the hand.
3.3.1 Small Three Winds, 30 points - consider if you have two wind pairs early on.
4.2.2 Three Concealed Triplets, 30 points - consider if you have one concealed triplet and one pair early on. This means that you must have three pungs concealed when you go out. Do NOT call for a kong on a discard if you are even thinking of going for this.
6.2.1 Small Three Similar Triplets, 30 points - This means you end with two pungs and one pair of a number, all of different suits.
These are the kinds of patterns you should be going for in nearly every hand of Zung Jung until you learn when it's best to do otherwise.
Keep playing!