My advice would be to determine first which airline is your best option. This will depend on your home airport(s) and where you want to fly to. Different FF programs have different advantages and downsides with regards to routes, partners, redemption options, fees, etc. Read up on any that interest you and see which works the best for you.

Then see what offers are out there that may give you the best sign-up bonus. Keep in mind there are flexible-point rewards programs, such as AmEx Membership Rewards and Chase Ultimate Rewards, that transfer to a number of FF programs, so don't overlook those.

Assuming you have good credit and the ability to meet any minimum spend requirements, find 2-4 good offers, pick a date and knock them out one after another (note that this may or may not work if more than one app with the same bank, i.e. Chase). Then, work on your minimum spend to get the bonuses. Most importantly, pay off all balances entirely every month -- paying interest is not worth it.