You should try Eva Kiss games then. In both Good Girl Gone Bad and Our Red String there is significant branching that has major impact on who the MC is and the story over all. That's just one dev as an example, I could offer many more but don't want to write an extensive plug for other games. Of the games I'm currently following I would say that BaDIK offers the least significant choices or effective branching. This really is a story on rails.
I have nothing bad to say about Eva Kiss, and I loved Good Girl Gone Bad when I played it a couple years ago; I really should try it again now that it's finished.
As for being on rails, it depends on how you look at it. BaDIK is far less flexible than GGGB, but it also has a much stronger emphasis on the overall narrative; it can afford to build up themes because it knows you'll encounter the setup and payoff. I think which is better will vary based on what you want out of a game. (It's also possible BaDIK will eventually encompass changes on par with GGGB, but it will take a long time to get there and I wouldn't bet any money on it.)
Just dropping a note that this game has made me interested in VNs in general, not just lewd shit. Very nicely put together. I played once, then went on monogamous runs with each and total dik fuckboy run as well.
I am resisting AL based on reactions. Shit I had a hard time with Melody. The first adult VN I have read. Got the family ending and my heart was broken for her lost dream. With how compelling good writing is in these I really don't want to mourn a death.
AL starts off with some minor dark elements, but it gets extremely intense by the end of it. It's a good - if
deeply flawed - game, and you WILL read spoilers if you stick around here for any length of time.
So if you think you'll ever be curious about it, I'd recommend girding yourself up and playing it once (with full knowledge that the game is trying to emotionally scar you). If you're perfectly happy to learn the details without ever playing in, then steer clear.
If you play with an MC whose sole rule is to never knowingly hook up with someone in a committed relationship or to pay for sex, then which girls/scenes does that rule out?
1) Josy on their dinner date (Ep. 4 and later is OK)
2) Sage as fuck buddy (Ep. 7 and later is OK)
3) Jade
4) Quinn's restaurant (can still hook up with all of the girls except maybe Riona)
5) Nicole/Envy (perhaps an exception, depending on how you classify a private lap dance that kicks things off)
6) Bella (perhaps an exception, depending on whether you feel she's in a relationship or not - she certainly thinks she is)
7) Lily (if DIK, need to pay her for scene during prep party free roam, but not if neutral)
Have I missed any? I'd think everyone else is fair game.
It might be faster to list the lewd scenes you CAN participate in. You're basically limited to Jill and Cathy full time, plus the one-shot with Nora. Maya's early scenes technically qualify, which means she and Josy post-Episode 4 might be okay too (it depends on how you consider the decision to try for something more). Sage would be fair game starting in Episode 7.
Quinn's rooftop scene in Episode 4 is in, but her other scenes would only qualify if you are allowed to join Quinn's restaurant, which seems dubious. Camila (and Mona), Riona, Lily, Sarah and Mel have a subset of scenes that don't require money (assuming you can qualify for them). I guess Becky would be okay (you need to be a DIK, which isn't too hard by Episode 7). If you really want to split hairs, I think you can watch the Pink Rose girls dance without paying if you let Derek handle the sex stuff in Episode 3, but I may be misremembering.
That's about it.