You will want to start with the Chase cards since Chase has heir 5/24 rule. They have a number of cards that you cannot get if you have had more than 5 new credit card accounts from any issuer in the past 24 months.
If you are able to make use of SW flights then there is simply no better travel deal out there than earning a SW companion pass. This is coming from someone who has been playing this game for several years but doesn't fly SW ever. We are in it for first class international flights with lie flats seats. Fortunately, we have a number of experienced people who know all about the how and when to earn your SW companion pass to make the most of it.
Discover is a cash back card. In my experience I get far less value on a cash back card than I do with one that earns points and miles. 100,000 points on a cash back card will get me a $1,000 statement credit. It can't buy me the $7,000 flight to Paris in first class. I have been able to get that $7,000 flight with 50,000 Chase Ultimate Rewards points transferred to United and booked a saver award flight. Don't get me wrong, I firmly believe in diversifying the miles and points portfolio but not at the expense of a 5/24 slot or any other slot that will get me a return that is greater than .01 cents per point. I only play around with cash back cards when I have plenty of variable points and miles to cover upcoming plans and find a specific need for one and the timing works out. I picked up the Bank of America travel premier card last September to get myself a $500 discount at Victoria & Albert's. I just picked up a Wells Fargo Propel card to fund some bank bonuses so I can do some extra shopping at Tokyo Disney Sea this June. Before that, the last time I picked up any cash back cards was in 2015 to get $3,000 in
Disney cruise excursions for free.
Cash back cards are few and far in between for us. We also don't stay under 5/24 and therefore don't churn any of the Chase cards. There are many on this board who do work to get under 5/24 to churn Chase cards. We blow through too many points and miles each year to make that feasible so our Chase cards are keeper cards. That said, we do apply for and cancel 5 - 8 cards every year. When I started this hobby in 2012 my score ranged from 690 - low 700's. It is now consistently over 800. Your score takes a small hit with a new application but the new credit line lowers your overall utilization ratio which increases your score. Cancelling newer cards won't affect your score much, cancelling an old card will.
Start with a plan of where you want to go. Plan two years out at least. Do a mock booking of where you want to go so you can see how many airline and hotel miles it will take and on which airline. Then take at least a year to get those miles and points in place so that they are where they need to be about a year before you travel. Hope that helps
@karmomof3