I thought you wrote that you found a board (pcie card) that has both USB 3 and SATA 3. Sorry if I misunderstood. I think you are asking if you should get a USB 3 card or a SATA 3 card, right?
I have an old computer without USB 3 and I bought a USB 3 card for it. I also bought an adapter that has USB 3 to SATA 3 for 2.5” drives (5 watts max). StarTech model USB3S2SAT3CB and it is around $11 USD. If you need to attach larger size 5.25” SATA drives you have a few options. You could open up your computer case and plug the drive in temporarily to work on it, or you could get a SATA PCIE card, or you could get a SATA dock with USB 3 plug and use it with a USB 3 PCIE card. I think USB 3 card is still the best option because USB 2 is so painfully slow compared to USB 3 and you can still use SATA devices in the various ways I described.
Important things to remember:
You’re USB thumb drives will still be very slow (at USB 2 or less) if they are not USB 3 thumb drives. You must use a v3 thumb drive in the v3 USB port in order to get the USB 3 speed.
Even if you have a SATA 3 drive and you plug it into your existing motherboard SATA 2 port, you will not suffer much loss in speed. The Samsung 850 evo with SATA 3 is 540 MBps, and if connected to SATA 2 it will be probably around 270 MBps or half the speed it should be. But, a USB 3 upgrade will increase your USB speed about 10 times! (and remember you can get a sata adapter or dock that plugs into the USB 3.