[D&D Basic] Should I impose limited choices as a DM ?

For a beginner - a good rule of thumb is the 'Rule of three' - if you want the players to know about something - have three ways they can/will learn it.

Want them to go do the dwarven mine? A quest to find a lost village boy (#1) was last seen at the mine. The local blacksmith could use some ore only found the mine - no one goes there anymore due to spiders (#2). The orcs the party 'encounters' after leaving the village have a half burned map that leads to the dwarven mine (#3).

The trick is that they might find all 3 pieces - they will most likely only run into one of them (or figure out what the significance is). If the info is critical to the story then increase this # and have sources that are actively trying to give the info to the players - otherwise it's highly likely they will take that right at Albuquerque instead of left.

I believe we do understand, in the solo adventure you would have something like at door, if the player try to listen to the door go to #3, if they open the door go to #8, if they look for trap go to #12. Those are his only 3 choice and that's a safety net for a new DM. But that's not how a group will work, what if one decide to knock at the door, what is one use spikes to keep the door closed and just skip it, what if they decide that they don't want to dies and go fishing instead.

And as a DM you will have to adapt and it may seem scary, but we all started where you are at some point (for some of us that was a very long time ago), the most important thing is "DON'T PANIC", you'll make mistake, you'll learn from them and you'll get experience.

Finally the most important thing to remember is to have fun :-D

The rules themselves do not place limits on what characters can do. Now as should be obvious, the solo modules are designed more as a choose your own adventure book that was also popular back then and is still the primary method used in video games. They limit the choices because they have to be able to provide a way forward with every choice the player makes. In a "normal" adventure, the DMs job is to facilitate a story that is collectively being told by the group with the PCs as the stars.

The boxed sets were designed to help both the players and DM to learn the game slowly, introducing new rules/concepts as they go, rather than throw everything at you in one book and expect the DM to decide what parts they were comfortable with running/teaching players. The rules themselves generally don't limit what PCs can do beyond what abilities they can bring to bear. Obviously, a wizard can't cast a higher level spell than his current level allows, but players in Basic can't even be tempted to try since those spells don't even appear until a later box. Basic also tends to limit the choices just by always being set in a dungeon. The layout limits their choices of direction of travel and everything is already mapped out. You don't have to deal with the party going in a direction you had not prepared for as you might in an Expert adventure where wilderness travel becomes a thing. Many modules may offer guidance on what to do if the players do X or Y, but obviously can't account for every possible option. If the module has a trapped door, the trap is explained, what rolls need to be made to spot and disarm the trap, and what happens if the trap is triggered. OTOH, there is no provision (in the module) for the players to do something clever like bust through the wall rather than use the door. This is a case where most DMs, especially new ones, would probably just say, "you can't do that," whereas a more experienced DM might be more willing to roll with it. Most modules written for basic also assume the monsters remain static, waiting for the PCs to discover them rather than reacting to sounds and coming to investigate. This keeps things more manageable for new DMs who only have to worry about the current room based encounter they are running rather than managing an entire level's worth of monsters simultaneously. More experienced DMs might look to make things "more realistic" by having the monsters react because they are more comfortable with the rules and therefore able to take things "off script" easier.

TL,DR. There is nothing in the Basic rules that would require you to create an adventure with pre-defined character choices and doing so would actually be counterproductive to teaching players how to play an RPG.