Just wanted to give my opinion since you are looking to write a gamebook- I have a few stories I’ve had in the works for a while, most of which are being continually worked upon, but I did submit a finished gamebook a few years ago to Windhammer which received mostly positive reviews. Basically I’m no Gavin Mitchell/ Robert/ Ulysses AI, haha, but hopefully I can provide some constructive feedback.
Before focusing on a setting, try to think about the different paths available to the reader and think what would lead to the most exciting scenarios- linearity is always to be avoided, but then again too many dead-ends/ instant death pathways can also spell the instant death of your story! My favorite example is based on the gamebook “Trial of Champions” (the sequel to Deathtrap Dungeon). By the time I had cracked how to beat it, I had played through it so many times that it was no longer enjoyable, and reaching the end felt more like a chore than a climactic finish. In that gamebook there are so many vital items needed that missing one automatically leads to failure down the road. I would stay away from this in general for whichever story you plan to write! You can use Twine or a different type of software to keep track of your pathways if it helps, and also what items are needed to progress to certain areas (if at all).
Like any story, gamebook or not, interesting characters, settings and plot lines also need to be a focus. What are the motivations of the character? Why should we care? Do their actions make sense in the grand scheme of the story? Saying that let me comment on your proposed ideas:
Halixor's Gauntlet A tried and true gamebook formula, and honestly one I will always enjoy. Deathtrap Dungeon will forever be a fan favorite, but if you do decide on this route try to add your own spin to it (the outside setting probably won’t be enough to give it flavor to be honest, and setting in an outdoor maze is also something we have seen before and that I wouldn’t necessarily recommend).
Trial by Ice Sounds similar to the beginning of “Portal of Evil”, another fan favorite about a down on his luck adventurer. Has potential, but again, unless you can add a new dimension to the storyline to make it “pop” it may be best to stay away, as to not rehash an old idea.
The Dragon's Hoard Interesting premise, but try to avoid making things to complicated, both for the reader, and for yourself the author. Also sounds similar to the “Hobbit” trilogy, so again try to avoid re-hashing stories that already exist, or taking the same storyline and slightly tweaking it.
My biggest piece of advice is don’t feel as if you have to be caged in by the fantasy genre- if you want to stick to fantasy that’s absolutely fine, but keep in mind that all sorts of gamebooks/ stories exist (case in point, the latest update to the site is a story about a 40 year old guy at a music festival combating depression and alcohol consumption).
All three of your ideas have merit, but if you decide to stick to one of them do try to make the story “yours” and as original as possible. Hope this helps!
what a thoroughly odd gamebook. i was tortured to death by a dom dwarf. i enjoyed it though. the gamebook, that is. i might enjoy the torture too, but that's another matter.
You've picked up on something a few other readers seem to have missed...
SPOILER
It's not hard to complete The Dead World. The whole point of it is to gain a large boost to one of your stats. If you completed the book and didn't find anything like that, you indeed missed out on something. Since there are four directions you can explore, there are probably four types of power-up available...or maybe one direction is fruitless...I can't remember anymore.
In addition to the good advice above, I would add that you should perhaps think about the length of each adventure and begin with the one that is likely to be the shortest. My reading of the three ideas gives me the impression that: -The Dragon's Hoard would be the longest adventure with the most things to keep track of. -Halixor's Gauntlet can be as long as you want it to be, although the longer it is the 'richer' the story will need to be to avoid it just being a series of rooms that ends up becoming tedious. -Trial by Ice is the simplest premise and one that can work as a short adventure. I would avoid the temptation to do too much world-building and keep all of your story branches parallel rather than divergent.
Obviously, I am recommending Trial by Ice, although possibly lesser in scope than you may have been imagining (you can also create sequels to enlarge the world later, perhaps writing an entire series and maybe even finishing it instead of leaving everyone hanging...). To help limit the scope and add an interesting angle to the story, you could have the Champion of the Lightning Goddess look on the main character with utter contempt, offering no explanations, just a stipend to accompany him/her. Part of the plot can be uncovering what the Champion really wants you to do and why you were chosen. The point of all this or a similar idea is to give the story a central plot beyond the quest itself, and allows the plot development to be more than just a series of events/enemies/traps, etc.
I don't think the protagonist of Day in the Life is combating alcohol consumption, Inebriation is meant to be your high score. I had the idea for a Day in the Life II where our thirsty hero explores the outsider art scene of Wolverhampton and Birmingham, but meanwhile the second mission of New Day Rising is reaching within measurable distance of its end.
killed by a vampire, oh the indignity. this was a fun gamebook, well plotted. some of the text is a little hammy, but it doesn't hinder it once you get into it.