Smart cards like Icoca, Suica and Pasmo are generally valid across Japan, so don't worry about which one you buy. You can use Icoca/Pasmo/Suica for all trains, subways and buses in Osaka. You can also use Icoca/Pasmo/Suica at many shops, especially convenience stores.

Yes, you can absolutely use your Suica (including Mobile Suica and the Welcome Suica) in Osaka and throughout the wider Kansai region. Thanks to the Nationwide Mutual Usage Service, Japan’s major IC cards are almost entirely interoperable. While ICOCA is the card issued locally by JR West, your Suica will work seamlessly for nearly all trains, subways, and buses in Osaka, Kyoto, and Nara. You can also use it as an "electronic wallet" at convenience stores, vending machines, and many restaurants. The only real limitations are that you cannot "return" a physical Suica for a refund in Osaka (that must be done in the JR East/Tokyo region), and you generally cannot use it for continuous travel that crosses between different regional company boundaries (e.g., taking a local train directly from Tokyo to Osaka). If you have a Mobile Suica on your iPhone or Android, you can even top it up using your credit card while standing on an Osaka station platform, making it the most convenient way to navigate Japan's second-largest city.