If you're playing an Assassin, and you frequently get the opportunity to assassinate, don't forget how powerful Action Surge is.
On your turn you make your attack as normal, then with your action surge you ready an action to attack as soon as someone else begins a turn.
A level 5 Assassin with a Rapier is going to strike for 3d8+6d6+4 when assassinating (1d8 booming blade, 2d8 rapier due to crit, 6d6 from your 3d6 sneak dice critting) for an average of 38.5. Then each round you'll be dealing 2d8+3d6+4 or 23.5
A level 3 Assassin 2 Fighter with the same stuff will strike for 6d8+8d6+10 (2 lots of 1d8 booming blade, 2d8 rapier crit, 4d6 sneak dice AND dueling style; but no feat to bump dex) which'll average 65. The other rounds you will deal 2d8+2d6+5 or 21.
As a level 20 Assassin, you'll be looking to death attack for a Booming Blade strike with your +3 Rapier to deal 6d8+20d6+8, all doubled by death attack, for 210 points.
However... if you went Half-Orc Sword Bard 9 Assassin 3 Gloomstalker 3 Echo Knight 3 Paladin 2 you'd be able to score 27d12+2d10+88d8+162 damage, which averages 767. This is achieved by:
1. Half Orc adding an extra dice of weapon damage on crits, so each greataxe is 3d12 (av 22 through fighting style)
2. 8 Divine Smites, using 1 6th, 2 5th, 3 4th and 3 3rd level slots for 38d8 (3rd level is 4d8 smite, the rest are 5d8)
3. Sword Flourish and Dread Ambusher bonuses total 1d10 and 2d8 since one is once per turn the other per action.
4. NO SNEAK DAMAGE because you're using a greataxe
5. Great Weapon Master Feat, +3 weapon and Str 20 in the calculations.
6. GWM feat bonus attack is the 9th attack.
This is entirely to help you avoid worrying about number crunching, because while it's fun to theorycraft insane damage rolls (also please note the above involves NO SETUP since that's pointless in these situations) just stick to playing what you'll find the most fun.