Whether you start as Rogue or Wizard depends primarily on what saving throw proficiencies you want more.
Remember that when multiclassing to Rogue, you pick up proficiency in "Light armor, one skill from the class’s skill list, thieves’ tools", but when multiclassing to wizard, you pick up nothing. So your choice comes down to one of two packages:
Rogue first:
Armor: Light armor
Weapons: Simple weapons, hand crossbows, longswords, rapiers, shortswords
Tools: Thieves’ tools
Saving Throws: Dexterity, Intelligence
Skills: Choose four from Acrobatics, Athletics, Deception, Insight, Intimidation, Investigation, Perception, Performance, Persuasion, Sleight of Hand, and Stealth
1 extra HP
Wizard first:
Armor: Light armor
Weapons: Daggers, darts, slings, quarterstaffs, light crossbows
Tools: Thieves’ tools
Saving Throws: Intelligence, Wisdom
Skills: Choose two from Arcana, History, Insight, Investigation, Medicine, and Religion and one from Acrobatics, Athletics, Deception, Insight, Intimidation, Investigation, Perception, Performance, Persuasion, Sleight of Hand, and Stealth
Both packages are fine. Rogue first gives you more ranged weapon options, but you don't much care because a Bladesinger gets extra weapon proficiencies anyway (e.g. longbow for long-range combat and net for restraining enemies; or you could pick up rapier if you want to use your sneak attack die more often with melee cantrips). If you think the campaign will feature lots of AoE and Dex saves then Rogue is obviously stronger; ditto if you plan to play often with caltrops and ball bearings. (It can be convenient to be nigh-immune to your own DC 10 Ball Bearings so you can scatter them all over the place with impunity while scouting.) But if you're playing in Ravenloft and/or are worried about mind control, and don't want to rely entirely on Counterspell, then wizard-first for Wisdom saves might make more sense. Also, wizard-first gives you a wider variety of skill options (e.g. Arcana), but that probably doesn't matter much because backgrounds already give you a wide variety of skill options.
And yes, the described tactics work well for a pure rogue as well. In many ways a pure rogue (non-Arcane Trickster) is even more reliant on them because he doesn't have options for turning himself invisible or teleporting away from danger. Skulker is an excellent feat for a rogue who likes to scout ahead of the party. (It would be good for a Shadow Monk as well, except that Shadow Monks just use Cloak of Darkness to turn themselves invisible. Also, they don't have Cunning Action, so they can't exploit Skulker as thoroughly during combat.)
Key advice for an advance scout: know what you can handle alone and when to go back for the party.