Well, if you want to split hairs, Death Attack reads
If an assassin studies his victim for 3 rounds and then makes a sneak attack with a melee weapon that successfully deals damage, the sneak attack has the additional effect of possibly either paralyzing or killing the target (assassin's choice). Studying the victim is a standard action. The death attack fails if the target detects the assassin or recognizes the assassin as an enemy (although the attack might still be a sneak attack if the target is denied his Dexterity bonus to his Armor Class or is flanked). If the victim of such a death attack fails a Fortitude save (DC 10 + the assassin's class level + the assassin's Int modifier) against the kill effect, she dies. If the saving throw fails against the paralysis effect, the victim is rendered helpless and unable to act for 1d6 rounds plus 1 round per level of the assassin. If the victim's saving throw succeeds, the attack is just a normal sneak attack. Once the assassin has completed the 3 rounds of study, he must make the death attack within the next 3 rounds.
If a death attack is attempted and fails (the victim makes her save) or if the assassin does not launch the attack within 3 rounds of completing the study, 3 new rounds of study are required before he can attempt another death attack.
So the attack must be with a melee weapon not a melee attack. Can you make a ranged attack with a melee weapon? Yes, all thrown weapons are still melee weapons.
Melee weapons are used for making melee attacks, though some of them can be thrown as well.
You could even throw a non-throwing melee weapon....
Thrown Weapons: The wielder applies his Strength modifier to damage dealt by thrown weapons (except for splash weapons). It is possible to throw a weapon that isn't designed to be thrown (that is, a melee weapon that doesn't have a numeric entry in the Range column on Table: Weapons), and a character who does so takes a –4 penalty on the attack roll. Throwing a light or one-handed weapon is a standard action, while throwing a two-handed weapon is a full-round action. Regardless of the type of weapon, such an attack scores a threat only on a natural 20 and deals double damage on a critical hit. Such a weapon has a range increment of 10 feet.
...and the Throw Anything feat should remove the -4 penalty.
So a thrown weapon is still a melee weapon (but not melee attack), and Death Attack requires the use of a melee weapon (not a melee attack).
The attack must still be a Sneak Attack, so Sniper still helps out by extending the normal 30' range for Sneak Attacks.
For the Ranger side, I like Infiltrator or Urban Ranger.
I would actually really recommend against playing a rogue (class) even if you want a sneaky assassin. Rogues generally start running into problems hitting their targets, and a lot of the Rogue Talents are highly situational, not helpful, or (in the worst cases) actually hurt you. And while they get more base skill points than any other class, the slight hit you'd take there by playing a ranger, alchemist, inquisitor, or bard is made up for by the skill points of your other party members and spells you/your party has available. Even moreso when you take into account that you drop back to 4+Int when you go into assassin.
What I would suggest, if you really want to keep the sneak attack dice, is to go with the vivisectionist alchemist archetype since you get 4+Int skills on a semi-Int-based class, and ways to make yourself and your party stronger through your mutagen (for yourself) and your extracts/infusions. Also, as a rule, Discoveries are always better than Rogue Talents (even the ones with expensive material costs are better because they at least do something useful).
If an alchemist isn't what you're looking for, then as I mentioned, rangers, inquisitors and bards (if you're looking to avoid performing, take the archaeologist archetype) also make good sneaky people, and ninjas are at least significantly better than rogues if you want to go that route.