As something being used in a figurative sense, I would say that none of those words are particularly idiomatic in the particular sentence construction in the question.
They might be used in some other figurative constructions:
This is the start of your life down an academic path.
She didn't take the easy road.
That choice was a one-way route to disaster.
He had many trials and tribulations along the way.
However, in terms of the actual example sentence, the following would be more natural:
You're going to work, study harder; and then you'll take the entrance exam again. So, be hopeful! You're just at the beginning of your journey.
Examples of this can be seen many places.
From "This is just the beginning of your journey!" at Carrington College:
You have chosen to further your education at Carrington College California – Online. But gaining a new qualification is just the start of your new adventure. Your journey has begun, but now is the time to plan your next steps, and map out a career path if you haven’t done so already.
From Lao Tzu at Brainy Quote:
Do the difficult things while they are easy and do the great things while they are small. A journey of a thousand miles must begin with a single step.
From "The Beginning of your Journey" at Balancing Mind, Body & Soul.
To start on your journey means having the maturity and courage to take 100% responsibility for your life and everything contained within it - your health, your career, your finances, your relationships, your emotions, your habits, and your spiritual beliefs.
From "Your journey is just beginning: A letter to the parents of children with CP" at the Cerebral Palsy Association of BC:
To the parents who just found out their child has cerebral palsy: I know that this may be a hard pill to swallow, but your journey is just beginning.
You probably will hear the word “never” a lot in the beginning of your journey with cerebral palsy. Or you may have heard that there is a possibility that your child may not be able to accomplish many things. Maybe you even hear that they will not be able to do the things that you expect for them to do. But I’m here to tell you that they will be able to soar their wings – although it may take them awhile to adjust to things. It’s going to take a lot of patience and a lot of physical therapy. For the most part, they will be able to succeed in anything that they reach for.