If this is a MacBook (13-inch, Early 2009), it cannot run anything later than El Capitan. Although you may be able to make connections to https sites, the versions of Safari and other browsers that run on El Capitan are ancient – and may not be very useful for browsing the Web.
I don't think you have a MacBook Pro (17-inch, Early 2009) or a MacBook Air (Mid 2009), especially since you say that your machine is white, and they had aluminum cases. It wouldn't matter, as they also are limited to El Capitan.
Among major browsers, Firefox has by far the best record of supporting old versions of macOS. But El Capitan is so old that Firefox 78 ESR for El Capitan stopped receiving "critical security updates" nearly five years ago.
Mozilla Support – How/where to get Firefox 78
Mozilla Support – Firefox Mac OS X 10.9, 10.10 and 10.11 users move to Extended Support Release
"Up until October 2021, we were updating affected users with critical security updates through the Firefox ESR channel, to help retain the best possible security. After this, no security updates will be provided."