While I prefer a combination of the two paths, I lean the most strongly on the reading passages one. Stories are nearly always more interesting than mere lists of words, and yet, phonetic lists such as Victory Drill can also be really helpful. I used Victory Drill a lot when I taught grades 1-2 and found that a daily short practice really helped most students become more fluent. But I think reading “real stories” — which are the true intent of reading those lists — will nearly always be more meaningful and hence, in the end be more effective.
While the approach must be tailored to the child’s academic level, I think it is also very wise to include their interests as much as is feasible. If possible, I recommend students read chapter books versus only short stories — they usually create deeper interest. To practice extra fluency the child could choose a favorite paragraph or half page from that day’s reading and go back to then practice just that section repeatedly before reading it to ____, someone who will happily enter into the pleasure of hearing the child read that section well and give needed affirmation. And key of course is regular practice.
One year I heard a (deeply) struggling reader was transferring to our school and would enter my room. When the mother asked for input I gave her a number of excellent chapter books on the second grade level and suggested she let him choose which one(s) look the most interesting and have him read a bit each day. For him, that approach worked very well. I don’t think simply reading short stories from a common reader would have created the same interest. And since he got to help choose which books to read according to what interested him, he progressed further. This especially worked well because this child’s mental development certainly exceeded his reading level and when interest is piqued, half the work is done.
On a bit of a different note: In the classroom I frequently assign a (different) half page of that day’s reading pages to each child, give them 2-3 minutes to practice just their section (repeatedly, with expression, asking me for any words they don’t know) and then they by turns come up and read their section in front of the class. In that way they practice fluency on a short section and then follow along as each child reads their section — they want to follow along because they want to know what is going to happen! They really enjoy this and I think it works well.