First, I'm a jerk. I have strong opinions about D&D and the TTRPG hobby. Most of the time my opinions are unpopular even amongst the most enthusiastic fans. Sometimes it's questioned if I even enjoy gaming at all.
To jump to the current situation and topic at hand. I've been asked to introduce a new player to D&D. She is enthusiastic about the hobby, watches Critical Role, etc., but has never played. It's important to me to try to put my biases aside and give this person a fair chance to fall in love with this hobby. I don't want my grognard, anti-WotC, anti-5E mentality to push away someone who could become a lifelong fan.
You on here wouldn't want that either, I'm sure. So I want to listen to your feedback and tips to help me get out of my own head and be welcoming to this enthusiastic new player. (She is a coworker of some of my other players.)
Hail fellow jerk!
I get it. The hobby has changed a lot over the decades, and some of us got stuck in the past. This person obviously trusts you to help, so I wouldn't worry too much about the differences in playstyle between then and now. I've been DMing a bunch of young whippersnappers with my 1E style for decades, regardless of edition.
Some specific questions...
5E or 5.5E?
Whichever one you are most comfortable with. Since there's a significant divide in groups about which to use (which reminds me of the 1E/2E divide), she's going to have to learn whichever system her regular group uses. I'd make sure to clarify which one you're using, so that she knows the difference.
No. She's going to want to learn how to play D&D, because that's what she's been watching and what she's most likely going to find a group playing. She can jump into OSR and Indy games later.
Start at 1st level or 3rd?
I
always start new players at level 1. I've heard arguments to the contrary, but it's easier to learn when they don't have too many abilities, and when they actually have to start a game, they won't be disappointed at a level 1 character.
Should I try to streamline the character sheet?
Here's where my old school grognardness comes in... absolutely not. I hate the idea of dumbing down the game for new players, because it assumes that they're stupid. Twelve year olds were expected to be able to figure out how to play a Magic-User back in 1E and BECMI, and the game rules have largely gotten simpler since then. She's going to struggle at first, but realize that if you use a streamlined sheet, she's just going to get confused later when she has a regular sheet.
I know a lot of players hate pregens, but I feel that they have a purpose with one-shot adventures. If she describes the kind of character she wants to play, you could easily make a pregen for her, allowing her to skip character creation. If she later decides she wants to continue to play, you can go over the rules on how you made the character.
Should I try the Starter Set? (I'm concerned because it's not really like how the actual game is played - with cards and components that don't really support the rest of the experience outside the starter adventure.)
I'd use The Lost Mine of Phandelver, regardless of using 5E or 5.5E, although you'd have to make some slight modifications for 5.5E. As a starting adventure, the first 2 chapters are solid, and I've used it a couple of times to introduce 5E (some new players, some from older editions). If you can't get a copy of it, I've heard Dragon of Icespire Peak is also good, but I haven't run it myself. In either case, I'd limit your plan to just a single session to give her a feel of what the game is like.
Are you running her solo, or do you have other players? If solo, I'd give her a 2 NPC pregen allies. You can go over their actions and abilities during the session, giving her an idea of what other characters can do. If a group, I'd probably limit it to only 2-3 other players, and let them know that it's primarily to teach the new player (so the adventure likely won't be completely played out).