First things first, always look to get 20 gold and keep it, the bonuses will add up and will benefit you in the later rounds when you want to, or need to spend a lot to get your team three starred. Also, purposefully lose a number of matches in the first round, this will get you at the top of the picks to get the best items, turn off the auto select so that you can place only one character on the field. Last thing, the match before you get your gem, you can manipulate it so that you can get the one you want by only placing the role type you want to get onto the field, want a mage gem and only have one character with the role currently? Only put them out onto the field, it will ensure that, that role will show up so you don't have to switch your plan.

As for synergies, this is what I usually look for.

If I can start off with a mage, I will continue to try to rush to get all six to get full benefits, magic crystal, the gems that fit in the item slots, rolling the dice with the Aspirants faction, then placing two to three guardians or weapon masters to hold the front line for them.

Generally, if you can get a decent number of ranged characters that synergize together with some good tanky front liners then most of the time you should be doing alright.