Recommended Cards
The following are cards I recommend you purchase. These cards would be considered cheap and somewhat powerful so you don't need to grind for hours to obtain them.
1. Jirai Gumo
Jirai Gumo is cheap and has decent stats associated with it. For only 80 starchips you are getting a monster with 2200 ATK that doesn't need to be fused. If you can get it early, it should help you through much of the mid-game.
2. Millennium Shield/Labyrinth Wall
While these cards won't do much for you in terms of ATK, they make up for it with their 3000 DEF stat points. These will cost 200 starchips each.
3. Parrot Dragon
Parrot Dragon is a cheap, strong Dragon card that will be useful for the usual Twin-Headed Thunder Dragon fusions. It will cost you 290 starchips.
4. Kaminari Attack
Similar to Parrot Dragon above, we are buying this card for Twin-Headed Thunder Dragon fusions. It will again cost 290 starchips.
5. Bright Castle
Bright Castle will cost you a smooth 800 starchips but is one of the best equip cards in the game. It can be equipped to any monster and will boost their ATK power by 500 points.