I won’t dissuade you from reading (listening) to Gibbon as he is something of a literary classic, but you must always be aware that Gibbon was writing two centuries ago and had his own ideological ax to grind. Historians today, drawing on a wider range of sources than Gibbon had access to, ascribe many developments in Roman history to very different factors than Gibbon claimed.
In fact, it is advisable to read several more recent works on Roman history first, so that you are then reading Gibbon purely as a literary classic and not as any authoritative source.
I think that's the wrong way around. Start with reading the canon, and then delve into its refinements (schools get that all twisted too, only introducing cannon at the graduate level). Reading Gibbon will give you a deep appreciation of his influence. In the process, you'll get a genuine step closer to experience the Enlightenment (imagine yourself in your salon, by candlelight, a gaggle of kids playing in the room next to you) as well.
_Especially_ so if you are reading out of a dilettante interest, rather than professionally.
That's all well and good, but OP seems to be interested in learning about Roman history, not 18th century English historiography. And for those purposes Gibbon is extremely unreliable.
Alternatively, you can get books about specific periods, like say late republic, and read those in sequence. But that takes more time.
Finally, and this is my preferred approach, get things written by Romans. Yes, they were biased too, and often quite obviously. But at least they didn't have stake in modern society and politics. As long as you pay notice to fact that they are mostly recording either hearsay, or propaganda, you should be fine. In that course I would recommend Twelve Caesars by Suetonius (hearsay) and Commentarii de Bello Gallico by Caesar (propaganda).
It's not always true, but it gives you a good idea of how they were thinking, what was their morality like and their values.
I've read Gibbon (the abridged version). How would you describe the axe he was grinding?
Also, in England in Gibbon’s day there was very little knowledge of or interest in Byzantium. That half of the empire lasted another thousand years in spite of a remarkably tight connection between church and state. Only the Western Empire fell in AD 496.