I will dissent with the folks who say don’t buy.
As Jim said, I’ve seen folks show up to classes with equipment that, well, they should re-consider using. However, typically it’s been very old equipment given to them by Grandpa Joe or bought for $5 at the corner yard sale. Any of those setups you mentioned will serve you well, and you can grow in to them.
You can’t practice or learn how to cast if you don’t have a rod and reel outfit. Not all classes will have gear for you/students to use. And, who is to know if the equipment they have is something that you will like or fits you?
So, summarizing, you’ve done an admirable job in identifying great rod/reel outfits that would be good all-around outfits for most folks. Besides, for many one of the fun things about fly fishing is buying new stuff. Guaranteed that whatever you buy, if you get in to this, within the next few years you will be wanting to buy more or additional equipment for various conditons.
Somone recommended the Sage Launch as an alternative to the FLi. The Launch is a little more flex than the FLi, and many intermediate folks not interested in distance seem to prefer that action.
Also, get a 4 piece for the travel flexibility it provides. There is very little difference nowadays in casting performance between the middle to upper quality 2 piece and 4 piece rods.
I don’t want to make this any more challenging or difficult for you, but if you are considering the FLi and the Launch, consider their Redington cousins, the CPS and the RS3, respectively. Some knowledgable friends consider them a better value than the comparable Sage models.
You really can’t lose with the selections you picked.
With a 5 weight, don’t get hung up on the reel. Be a little thrify on the reel, and spend the $$ on the rod and the line. DOn’t overlook the importance of the line; the line can be a HUGE factor in the performance of a rod.
I wouldn’t buy a Cabela’s reel; not that they don’t provide good value, but it will likely be discontinued in a year or two, and you won’t be able to buy parts or extra spools. Voice of experience here. Ross is a manufacturer that offers great value reels up and down the cost spectrum.
Good luck on your journey, and congratulations that your sweetie pie wants to also travel that road with you.