Core cubes are acquired from playing in arenas. You will get them win or lose, so play all three of your arenas and collect your cubes. Priority for using the cubes is Speed, Attack, Defense, then Hit Points. At levels 2, 5, and 8, the boosts will effect all of your toons regardless of their region. Boost every region to level 2 in speed before heading over to attack. Repeat that for defense then hit points. After all regions are at level 2, repeat the process to level 5, then 8.
Bravo to Scopely for making gems easy to get. Just because they are easy to get though doesn't mean you shouldn't spend them wisely. You will probably spend some gems in the Lucky Saloon, but don't overdue it.
Use 200 gems per day for energy. Only use the gems at a 50 gems:100 energy ratio unless really needed.
Use 7200 gems to buy 30 gold tickets. The cost per ticket is 240 gems. Keep that in mind while you are in the saloon while deciding whether or not you should pay to keep playing.
It is pretty easy to get all the gold that you need in the lower levels of the game. Later, you will find that you rarely have any gold and are spending upwards of 500k a day. Save your gold for as long as you can by not leveling your common and rare toons. Use it on selected toons to create powerful teams.
Gold tickets get you what you want in the game. They are used in special events and in a variety of wheels. To get the most use out of the tickets though is to save them for a PTL of a team you are trying to max out. To get the legendary of your team to 7.7, you will need several hundred gold tickets. Another great use for gold tickets is to purchase black tickets. Whenever you see a gold ticket to black ticket exchange, buy all of the black tickets available at a 3:1 ratio.
You get 25 Portal every time you complete a quest in the Endurance Tower. Portal can be exchanged for powerful toon pieces in the portal store. You can get up to 120 toon parts a day or more by doing the tower.
Special Core Cubes are acquired from playing in Alliance Wars. You will get them win or lose. At levels 2, 5, and 8, the boosts will effect all of your toons regardless of their region. Boost every region to level 2 in whatever stat you want to increase. Repeat that for all other stats. After all regions and stats are at level 2, repeat the process to level 5, then 8.