Building a Rogue / Thief as an Assassin, archetype options?

So I've been mulling over building a Rogue as an assassin, both with and without free archetype there's a lot of interesting possibilities.

Though I will say outright, the Assassin archetype (ironically) isn't that hot. Only the much later feats have a significant impact and even then are a hard sell compared to a lot of other options available at the same time.

Personally I've considered Thaumaturge, for an extra 2 damage on a hit and eventually getting an implement (Mirror for teleport and easy flanking, weapon for an attack of opportunity, etc). Fighter for more melee combat techniques. Monk for flurry of blows with monk weapons. Ranger. Alchemist (Though without toxicologist buffing poison DCs you'd probably be doing it for bombs instead). Shadowdancer is a great standout but is only available from lv8.

With that said if I am doing an AP with my group, we typically do not use FA for 'official' adventures. In which case I'd probably take Ancient Elf or something, for that which would be the most impactful and useful for just the dedication? Thaum for example just gets me, more or less, 2 extra damage on a target as the big selling point.

Assassin archetype isn't bad for rogues. Mark for death gives +1 precision DMG (+2 if your weapon is +3) against off-guard (flat-footed) targets whats is pretty good for thief builds that usually is focused in keep the target off-guard to get benefits from its class precision damage and gives deadly d6 to weapons like Shortswords allowing you to benefit from agile+finesse weapons with a good additional critical damage with them or make rapiers d8 weapons.

This IMO is already better than +2 from Thauma.

Expert Backstabber also increases the precision damage a bit.

Yet I agree that this archetype doesn't give much more for rogues.

Another option maybe get Laughing Shadow Magus instead and get Rogue or Shadowdancer/Shadowcaster archetype to improve your stealth abilities and give some precision damage too.

Assassin is good for FA rogues if you plan to grab more archetypes later on. Expert Backstabber at 4 and either Poison Resistance or Poison Weapon at 6 is a solid start (I personally prefer Poison Weapon, something that lets you capitalize on good scouting and prep is always great, and you want to do that regardless due to Mark of Death).

Later on there are multiple good options. Shadowdancer is neat, Kineticist can be absurd later on if you go for Air, Gunslinger is amazing once you reach lvl 12 due to Triggerbrand Salvo (maybe a bit too loud for an assassin, tho), spellcasting is amazing for rogues too... The list goes on.

For regular games I would skip Assassin, tho. If you want to archetype with Ancient Elf, my vote goes to either Psychic or Kineticist. The first gives you the good utility spell list(True Strike, Invisibility, Loose Time Arrow, Time Jump and Haste are both effective and fitting for an Assassin) and and some neat focus spells (Guidance and Shield are so, so good in general). Kineticist gives you a really potent tool in Clear as Air at lvl 12 and access to Four Winds early on. Cyclonic Ascent at 16 is decent, but not as impresive as the non-archetype version at those levels.

So I've been mulling over building a Rogue as an assassin, both with and without free archetype there's a lot of interesting possibilities.

Though I will say outright, the Assassin archetype (ironically) isn't that hot. Only the much later feats have a significant impact and even then are a hard sell compared to a lot of other options available at the same time.

Describe what it means for a character to be an assassin.

Because that can mean different things to different people. Some of them are able to be represented in the game mechanics, and other assassin concepts really aren't.