Writing about thieves/tricksters and their surprise bonus made me think about another class that traditionally had a surprise bonus: the ranger. I don't want to use the traditional ranger class directly; it's too power-heavy. Plus, part of the essential nature of the ranger -- wilderness knowledge -- is better handled as a background. Fighter + ranger background is a reasonable replacement for the ranger class. But what if someone wants a ranger feature they consider "iconic"?
Woodland Archer and Favored Creature Opponent are the easiest to implement; just add another background or two (Archer, Humanoid Hunter.)
Dual Weapon Fighting: I've heard people talking about how dual-weapon rangers are iconic, but never played a version of D&D that included them. I'm inclined to interpret using two weapons differently; fighters or those with a Dual Weapon background would get a bonus to their attack roll and could choose the most advantageous weapon to strike with. I might even allow players to pick up simultaneous attack and parry as an individual talent later.
Surprise: Traditional 1e rangers are surprised less often and surprise others more often. The safe way to do this is with a simple +1 bonus if the ranger has more background experience than the opponent. Another option, though, would be a hybrid Fighter/variant Trickster, with the scaled ability changed from a bonus in subtle and sneaky situations to a bonus in wilderness survival and stealth situations. That's a bigger bonus at higher levels, but applies only to wilderness situations.
Animal Companions: If an escalating bonus isn't imperative, rangers can simply take an Animal Trainer background. Beast Masters, either the mundane or supernatural sort, would be much better at this, so a player who wanted to focus on this could just take Hybrid Fighter/Charmer (beasts) or Hybrid Spirit-Worker (beasts)/ Charmer (beasts) with a Ranger background.
Access to Magic: I'm not so attached to this, but I think druidic spirit magic could be handled as spirit intervention for non-spell casters (basically, reaction roll for spirits modified by spell level requested.) Magic-user spells could be limited to individually learned out-of-class spells.
I think the short answer for "how do I play a ranger?" is as a hybrid of Fighter and either the variant Trickster (wilderness survival) or Charmer (beasts) (or a mix of both!) with a Ranger background and, if necessary, additional backgrounds.