[RPG] Are Constitution changes retroactive when calculating max HP

Each level, you get Hit Die + Constitution modifier additional Maximum HP. You always take the maximum of the Hit Die at 1st level; afterward, you may roll the Hit Die or take its average rounded up.

Therefore, with a 1d10 Hit Die and +3 Constitution modifier, assuming you take 6 each time instead of rolling:

\begin{array}{rrcrcrcr} \text{1st level:} & 10 & + & 3 &&& = & 13 \\ \text{2nd level:} & 6 & + & 3 & + & 13 & = & 22 \\ \text{3rd level:} & 6 & + & 3 & + & 22 & = & 31 \\ \text{4th level:} & 6 & + & 3 & + & 31 & = & 40 \\ \end{array}

In short, you will add 9 HP for each level beyond 1st.

If your Constitution modifier later changes, it will apply the new bonus for every level you had so far. So if at level 4 your Constitution modifier is boosted to +4 instead of +3 (for a difference of 1), you will add 4 HP because you are level 4, which will make your HP 44 instead of 40. (It's basically as if your Constitution modifier were +4 all along.)

I have few ideas based on your criteria but the best option really boils down to the situations the party finds themselves in and how the party functions in combat. Because of that, I'll list some options and give the pros and cons of each.

Idea 1: Monk 17/Ranger 3

(Take Hunter's Mark, Dueling, and either Colossus Slayer or Horde Breaker)

Possible Damage: 4d10+4d6+[1d8(CS)]+24 for 3 hours (Attack, Extra Attack, Hunters Mark x4 (each weapon attack) [, and Colossus Slayer])

Pros:

• Up to 3 hours of use split into up to 1 hour increments 3 times per long rest.
• Even if you are out of ki and Hunter's Mark uses, you still get Dueling bonus to weapon damage.
• Bonus 1d8 if target is under its max HP, even if you don't have ki or Hunter's Mark. (If you take Colossus Slayer)
• You can hit 1 additional target for 1d10+7 each. (If you take Horde Breaker)
• Ranger class features are nice to have for adventuring.
• d10 hit die

Cons:

• Hunter's mark only recharges on Long Rests and might be ended earlier than intended if you fail a concentration check.
• You don't get the full effect on the first round. You need to use your bonus action to cast Hunter's mark which means you don't get your bonus unarmed or Flurry because it requires a bonus action, only your 2 attacks +2d6 (+1d8 if you have CS and target is below max HP).
• Every time your mark dies, you have to use your next bonus action to pick another mark.
• Because Hunter's Mark is a concentration spell, you risk losing the effect if you take damage.

Idea 2: Monk 17/Fighter 3

(Take Dueling and Battle Master or Champion)

Possible Damage: 4d10+1d8+24 up to 4 times between rests or you run out of ki. (Attack,Extra Attack, Flurry of Blows, 1 damage dealing maneuver)

Pros:

• Superiority Die and Ki recharge on a short rest.
• Maneuvers have utility effects (Battle Master)
• Dueling
• Action Surge gives high burst potential once per short rest. (6d10+1d8+38)
• Second Wind (though 4-13 HP isn't that much at level 20)
• Proficiency with 1 artisan's tools. (Battle Master)
• d10 hit die
• Increased Crit Range (Champion)

Cons:

• You only get 4 rounds of bonus 1d8 damage.

Idea 3: Monk 17/Rogue 3

(Take Assassin or Swashbuckler)

Damage Potential: 4d10+2d6+20 (Attack, Extra Attack, Flurry of Blows, Sneak Attack)

Pros:

• Bonus damage not reliant on recharge. Only have to worry about ki
• If you don't have advantage, you can still sneak attack the target if one of your other party members is in melee range.
• Expertise (double proficiency bonus in 2 skills)
• (Swashbuckler) Sneak attack if no one else is within 5 ft of you.
• (Swashbuckler) Add your Charisma to initiative (if you want)
• (Swashbuckler) Your target can't make AoO against you.
• (Assassin) Crit on surprised target for 8d10+4d6+20
• (Assassin) Proficiency with Poisoner's Kit for potentially more damage or other utilities.

Cons:

• Smaller hit die (d8).
• Smaller minimum damage potential.
• Monk weapon must be finesse. (Not too bad, just limits weapon choice.)
• Can't sneak attack with unarmed strike
• Very reliant on party placement