Free checked baggage only applies to domestic flights for at least some of the airline cards.

If you're trying for one specific trip for multiple people, I'd be careful about getting spread too thin across too many programs. For example, you can buy AA flights with Citi TYP points, but you can't combine TYP and AA miles (at least not easily, as far as I can tell). You might be better off getting a Citi Premier now and then a Citi Prestige later (or two different Chase or Amex cards), so your points are consolidated.

Also, keep in mind that once you're past five credit cards in 24 months, Chase won't approve you for any of their flagship cards (Sapphire Preferred, Freedom, etc.). If you like Chase's program, start with them.