I've played in and run evil campaigns of various sorts in both 3.5 and 4e (though not 5e, I think my learning will transfer), and run into a lot of problems: My Guy Syndrome comes up a lot, as does a tendency to default to a regular D&D storyline only with more stealing of spoons and kicking of puppies to remind ourselves we're evil. Sometimes an evil campaign instead descends into over-the-top motiveless violence until there's no story at all. There's a whole host of at-the-table and in-the-story issues, and I tried many different strategies to address them. Eventually I came up with a framing device which works well for us in avoiding these problems:
Provide the PCs with a Master to guide them toward orchestrated works of Evil.
Start the game with the PCs as underlings/minions/hirelings/apprentices/etc of a powerful evil NPC. The Master has a complicated Evil Plan and he tasks his minions to enact various parts as the Plan progresses: "Bring me the soul of a hound archon," "Raze the border keep," "Steal the Apocalypse Gem," "Help a spy infiltrate the paladin's ranks," and so forth, tailored to the PCs' abilities.
This provides the party a reason to work together despite having different agendas (and working together will hopefully bond them as friends so that they want to continue as a group) and establishes small achievable evil goals that accumulate into an Epic Evil Event.
All you need to do is ask the players to make sure their characters have a good reason to work for the Master: The serial killer likes having his rampages subsidised (and the Master protects him from the Law); the necromancer seeks to learn from the Master's experience and gain access to his libraries of forbidden lore; the mercenary's in it for the money and benefits.
Eventually the Apprentices will surpass their Master.
Expect the party to betray their Master at some point, hijacking his Evil Plot for their own gain: this is not only expected, but awesome. It's the Master's Evil Plot, not yours, and the story isn't about the Master--it's about his apprentices. Consider the Master to be training wheels for evil, setting an example which the party can then follow to surpass and overthrow their instructor as they level up.
This works because Evil Needs Goals.
As Ed describes so well and AgentPaper elaborates in the D&D context, evil needs concrete reasons motivating its actions. The Master provides goals and motives while the players find their feet in the new paradigm, channeling and guiding their exploration of what it means to be evil in ways compatible with the D&D paradigm without simply kicking puppies during a dungeoncrawl.
A word of warning: Alignment is tricky.
D&D has a history of the details and nature of alignment sparking major heartfelt arguments, because D&D alignments are not easily (or appropriately) matched to real-world philosophies and moralities; they're narrative simplifications to support the game's conceits and draw their power from storytelling conventions rather than from genuine moral complexity. Exactly what this means and how to deal with it are beyond the scope of this answer (and possibly this site, although there's a LOT of questions on the topic you can look at), but you should be aware it exists and be ready to talk with your players about what "Evil campaign" means to them so there aren't nasty surprises mid-game.
Pretty much all rules dictating deity worship are gone in 4e, replaced with DM discretion and recommended threats of story-based consequences for unpopular actions or beliefs within a subculture.
Additionally, there is nothing in the rules preventing a character from worshipping multiple deities, cherry picking which parts of each that appeal to them. The PHB openly states, “Most people revere more than one deity” (PHB pg 20), but most people are under the impression that, because the online tools only allow you to select a single Deity, that players can only worship one. This is point-blank untrue, and furthermore, wouldn't make much sense within a provably polytheistic society.
So your character could worship Sune because she embodies the ideals of Beauty and Trickery, and another evil deity of your choosing that embodies torment and madness. The two would combine nicely in your concept.
Another twist I've used before successfully is a character who believes that she worships one deity, but who is in fact interacting with another entity entirely.
Perhaps the most well-known iteration of this kind of story arc is Pelor the Burning Hate, but it doesn't have to be a universe-wide deception by the deity, it could just as easily be a case of an individual or single temple being fooled by a fraudulent impersonation of their intended deity.
In this case, such a character could honestly believe that they are worshipping Sune, but their prayers are being intercepted and answered by Cyric, the Prince of Lies, who is attempting to gain enough influence to break free of the prison that Sune helped build for him.
His alignment could have aided in the slow corruption of your PC, and the illusions afforded him by the trickery domain would be neatly augmented by the madness and strife slowly creeping into your PC's demeanor.
It's up to your DM how to adjudicate things such as feats, paragon paths, or epic destinies which require one to worship Sune, but thankfully there's only one of each, and none of them are stellar picks.
Best Answer
It is possible for celestials, even the most powerful ones, to be tricked by evil deities. They might become pawns, initially unaware that they are being played with. They might eventually get corrupted and fall. A famous example is Malkizid, a solar who was seduced into betraying Corellon by Lolth, and was later cast into the Nine Hells. Another example (from 3.5e) of a celestial actively serving an evil power was Thah Rhalar, a hound archon minion of Set.
If you want some inspiration about how to modify celestials to serve evil deities, you might have a look at the description of angels serving the God-Pharaoh, who is actually the malevolent dragon Planeswalker Nicol Bolas, in the Plane Shift: Amonkhet write-up available as a free pdf from WotC. While not legal in Organized Play events, it is still some kind of "official" D&D-5e-compatible material.