I'd like to try and clear some of this up, since it's a bit hit and miss in this thread.
Beyblades are only compatible with other beys of their series, and launchers from the same series. Exceptions rarely exist, for instance some electronic Hasbro Metal Fight beys are compatible with Bakuten Shoot launchers and Hasbro's Luinor L3 is very picky when it comes to launchers in general, but aside from those rare exceptions any Burst launcher should work with any Burst bey, any Metal Fight bey will work with any Metal Fight launcher, and any Bakuten Shoot/HMS bey will work with a Bakuten Shoot/HMS launcher respectively. This is irrespective of brand, though Hasbro launchers in the Metal Fight and Burst era may struggle significantly with the heavier weights of Takara Tomy beys near the end of their competitive lineups, especially in Burst. They're simply not built to handle that sort of weight.
For previous generations (Bakuten Shoot/HMS/Metal Fight) the brands are cross-compatible. You'll be able to use Hasbro and Takara Tomy parts interchangeably with one another, with maybe the occasional mold difference at worst. For Burst this is not the case.
For Burst beys you have three different systems to work with: Hasbro's Mainline, Hasbro's Pro Series, and Takara Tomy releases (Young Toys also releases the Takara Tomy beys as an equivalent official brand). Of these TT and Hasbro's Pro Series are compatible with one another, but don't work properly with the Hasbro Mainline. In kind, the Hasbro Mainline doesn't properly combine with TT or Pro Series lines. The exception is disks and disk frames, which don't have any cross-compatibility issues regardless of which series it came from and are effectively universal parts.
Since the set you've gotten is from the Hasbro Mainline, you're probably going to find the most opportunity to mix and match parts (customization is a large focus of the game, building combinations of your own) with other Hasbro Mainline beys, as well as find more even fights since the Hasbro Mainline has been avoiding power creep like the plague. Takara Tomy beys from the God era (Evolution was Hasbro's rename if that season) will be a fair fight as well, but will lack cross compatibility short of the aforementioned disks.
I will say that the stats on the box are relatively meaningless as well, and mostly just give you an idea of what to expect. "Agility", for example, doesn't really make your bey any faster, and Weight as a stat doesn't always match up to reality (I've seen beys with a high Weight stat that actually weigh less than another with a far lower weight). It's far better to figure out what parts are good at what on your own, or ask around for advice if you need the help.
I of course know a fair bit about the game, of tops of all generations, starting my blading journey as a kid in the early 2000s. If you really need more help feel free to shoot me a direct message. Unlike some of the kids here I've got the knowledge to help you along in my experience, and recent tournament successes to prove it in the fledgeling yet competitively strong Indiana region.
Either way, I wish you luck out there.
Cincinnati-based Organizer, and owner of every single currently released TT Burst bey part in at least one color. Hard to think of anything I don't have from MFB either...