This came to my head when I tried to multiclass. If you wanted an Assassin, Would you choose Rogue, Fighter, Or multi-class both?

"Assassin" is a specific sub-class of rogue. If you want something else, literally any class can be called an assassin.

A pure rogue makes the best cinematic assassin that hides in the shadows, but a wizard with teleportation and magic missile would actually be a lot scarier.

Assassination is very focused on a single event, so a class that can burn all of its resources very quickly would be most effective.

I'd pick a Rogue Assassin, not whatever a "rouge" is. (Jk, spelling errors happen to all of us, it's just that I find the amount of times this one shows up to be incredibly annoying.)

I think the best way to play an Assassin is to take 5 levels of Champion, 15 levels of Assassin.  The assassin is strongest when he has Surprise, and this would give the assassin 4 chances to hit in the surprise round with advantage, and the dice lost on the critical only amounts to 4d6 (16d6 instead of 20d6 on the crit sneak attack).  However... you also get 3 more attacks with advantage and automatic crit (without sneak attack) in the first round, yielding a probable additional 6d6 +24 damage (from the ability bonus and +3 weapon at high level, for +8 per hit).  After the first round, you (probably) have an additional 2 attacks with advantage in the next round with normal sneak attack on one of them, but here's where the real benefit kicks in.  In normal combat you still have a 1 in 5 chance of getting a critical, instead of 1 in 20, because of the extra attack (level 5 fighter) and increased crit range (level 3 champion).  This means that over the course of the combat you will be doing significantly more damage (periodically getting another crit on the sneak attack), and the little that you lose on the sneak attack (2d6) would be made up for by the extra attack with d6+8, and 4 times the chance of getting a crit overall.  Even when you consider losing the Elusive and Stroke of Luck and Death Strike (double critical) buffs, you still gain more than you lose by multiclassing as a champion (plus more HP as well) with the extra attacks making up for the certain hit.  Only very few extra-planar creatures would have such a high AC that you would benefit more from Stroke of Luck instead of having the extra chances to hit and 4 times the chance to crit.

Of course, doing 40d6 on the Death Strike is hard to turn away, but you can still get it along with the double chance of crit in normal combat by only going to level 3 champion, level 17 assassin.  It is a bit of a toss-up on that one, and really depends on how often you think you will get surprise vs. having to slug it out in normal combat.  For most of the game, until you get to level 20, I think it plays out better having the extra attacks.

One thing I don't like about the Assassin subclass is that the name of the subclass makes a lot of people think that, if you want to play as an assassin, then you must play as this specific class and this specific subclass.

Not that the Assassin Rogue is a bad version of an assassin, but it's kind of... underwhelming? It has a truly amazing early level feature, but after you get the Assassinate feature, the other subclass features are mostly garbage. A false identity you could create with 25gp and a week of work? How often do you get a week of downtime in the middle of an adventure? The ability to imitate a creature, but you have to observe them for 3 hours? Any spellcaster with Disguise Self could do either of those easily as long as they had a decent Deception skill. It's a truly amazing Spy subclass for a hard, crunchy game with a DM who's very strict and plays a very realistic game, but 49 times out of 50, everything other than the Assassinate feature is useless... and even with assassinate, the best feature relies heavily on getting surprise, which is really hard if you're traveling with allies who don't also have amazing stealth skills.

Again, I know i"m talking a lot of shit, but Assassin is still overall pretty good. I think it's just over-represented for a subclass that's actually really hard to actually utilize in the game. I know that, as someone who played a two-year campaign with a player as a an assassin, the DM had to homebrew allow "surprise" to be a much looser concept just so the player could actually use their auto-crit a single time in the campaign, and even then she almost never got to use it. I think another good example is the first campaign of Critical Role, where one player was an assassin rogue and in that long-running campaign he only managed an auto-crit like... 2 or 3 times total, and one of those times was a deliberate trap set by the DM that made things several times worse.

If you want to be an assassin without being an Assassin - Shadow Monk or Gloomstalker Ranger fit the bill reasonably well. Soulknife is pretty good too since you can have all your weapons confiscated and still be quite deadly.

I'd say You could multi class Rogue and Fighter

Quote from BruenorBattlehammer_1 >>

This came to my head when I tried to multiclass. If you wanted an Assassin, Would you choose Rogue, Fighter, Or multi-class both?

 Rogue. Because at level 3 you can just pick assassin.

And it'd be bad to multiclass fighter, because one of the main benefits is better armor - but that's going to disadvantage any stealth you'd make as a rogue.