@MerricB touched on this above...but the most popular and widely played 5e adventures do
not follow the pattern everyone is repeating here.
LMoP: You get ambushed by goblins, track them back to their lair, and have multiple fights in the lair, plus possibly avoiding being hit by a flood. Level 2: You explore a town with a fair amount to explore, learn of and fight a local gang, find their hidden lair, fight more of them, and then have some side quests. Level 3: More side quests, overland travel, then Cragmaw Castle, from which the local goblin-kin king rules. (The sidequests in level 2 or 3 can include a dragon that can also easily kill the party).
For CoS, the deathouse lives up to its name. The opening of the Tiamat one is also infamous.
I say go with the popular route. Use level 1 and 2 and don't hold back. Which are the best point to come up with a new character, before getting too invested.