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I agree with most of the others here: It’s ideal to have both, but starting with Chase is a good idea for at least a few different reasons.
One of the big reasons to start with Chase is the 5/24 rule where they will not approve you for a new card if you’ve opened 5 cards (from any bank) within the last 24 months.
And, for Chase UR, you really only need one card that you’ll pay an annual fee on (generally either CSP or CSR) and then you can augment earning points to use through it with cards that have no annual fees, such as Freedom Flex and Freedom Unlimited (and, if you have even a small business, Ink Cash is also a great addition.)
You’ll likely eventually want to pick up some airline or hotel-specific cards and Chase’s 5/24 rule also applies to those (e.g. Hyatt, United, Southwest, Marriott, etc.)
That said, you can get just as much, if not more, value our of Amex MR points as Chase UR and it’s ideal to eventually have a decent amount of both, especially with Amex’s wide range of airline transfer partners.