Many good answers here, but let me give you one advice: Check out how your DM wants to handle stealth, it can be a world of difference on how strict or not he does check on that.
If he insist you cannot attempt to hide at all if there is the slightest chance some mob spots you, then rather go for Arcane trickster or swashbuckler. Arcane trickster could take invisibility spell, swashbuckler is basically a finesse fighter dressed up as rogue
If he goes the medium way, take the basics (burglar)
If he is superrelaxed on stealth and bluffing and other such shticks and if you are eager for much RP then try the assassin (who is less about assassin but more like mask expert and impersonator)
If he insist you cannot attempt to hide at all if there is the slightest chance some mob spots you, then rather go for Arcane trickster or swashbuckler. Arcane trickster could take invisibility spell, swashbuckler is basically a finesse fighter dressed up as rogue
If he goes the medium way, take the basics (burglar)
If he is superrelaxed on stealth and bluffing and other such shticks and if you are eager for much RP then try the assassin (who is less about assassin but more like mask expert and impersonator)