As
@CyndiLouWho said - Chase is a great place to start. The reason we don't like to put AU's on the account is the Chase 5/24 rule. Meaning Chase will not approve you for any of their Credit Cards if you have opened 5 or more Credit Cards in the past 24 months. (this is from any credit card company - not just Chase). So, many of us will alternate cards between Player 1 and Player 2 plus getting referral points on referral cards. Good thing is that most (not all - looking at you Cap One) Biz Cards do not count in the 5/24 rule. So, as long as you are under 5/24 you can keep getting Biz cards all day long. Most of use use that to our advantage.
Chase has so many great cards as does AMEX and others. Once you start - you just keep going. I am always working on a SUB (sign up bonus) as that is how you accumulate the most points. I, like many others on here like to diversify and get points from all different cards, as you never know what you might need when planning upcoming travel.
For example: Currently - I have the following between DH and I.
Chase UR's - 856,000
AMEX MR's - 600,000
Delta - 28,000 (If needed, I transfer from AMEX)
Marriott - 190,000 Plus 3 Free Night Certificates a year.
SW - 160,000 with 50,000 more coming soon. Currently I have Companion Pass that expires end of Year. DH will have his soon that will expire end of 2025. Then I will get again.
IHG - 210,000 Plus 3 Free Night Certificates a Year
Cap One - 122,000 (just used 100,000 to offset some flights booked)
US Bank - Had $1300 in Rewards - used for Disney Tickets. Have about $850 more coming soon.
Some on here - do much more than this. And some much less. We each go at a pace that is good for us. Don't be afraid to ask lots of questions - everyone is so helpful and better to ask in advance before opening any cards you are unsure of. Every card company has their own little rules that you will learn more about. But this is a fun hobby and have afforded my family so many trips we would have not otherwise been able to take.