lonelytraveler8 wrote:
Let me ask this about your examples, NileCat:
--->本を読みはじめる (Using a verb stem here, you just put the verb you want right after. Is this meant to be a correct example or incorrect? I couldn't really tell based on what you wrote)
--->本を読むのをはじめる (This appears to be what my book says. Is this also correct? What is the best and most natural form of all of these?)
At this stage, as NileCat-san says, it is more useful to understand the grammar ~Vはじめる/~Vだす rather than V+[こと/の]をはじめる to you.
Both ~Vはじめる and ~Vだす, ます form of V is used, are categorized as JLPT 3 grammar.
For example;
その女の子は泣きはじめ(まし)た。
その女の子は泣きだしました。
The girl began [to cry/crying].
The girl stated to cry.
-- ~V(ますform )+はじめる
-- 泣く→ 泣き(ますform)+はじめる=泣きはじめる
-- past tense →泣きはじめ(まし)た
-- 泣き(ますform)+だす=泣きだす
-- past tense → 泣きだし(まし)た
Let's review NileCat-san's examples.
NileCat wrote:読みはじめる/走りはじる/歌いはじめる/行きはじめる
"その女の子は泣く[の/こと]をはじめ(まし)た" is hardly used in a daily conversation. (When the verb is neither an intentional nor a conscious action, V ことをはじめる is an inappropriate usage.)
An inanimate subject works as well in both usage.
その電車は動きはじめ(まし)た。
その電車は動きだし(まし)た。
The train began [to move/ moving].
The train started moving.
If the subject of a sentence is inanimate, Vことをはじめました is weird in most cases unless it has a poetic/rhetorical intention. At least その電車は動くことをはじめた won't be replaced with その電車は動きはじめた.
In either case, grammar Vはじめる/Vだす is much more common and has a natural tone than Vことをはじめる.
As for your original, 本を読みはじめる is natural, whereas 本を読むのをはじめる is uncommon.
Hope this helps.

--
Edit: It seemed that I had taken too long to write this post.
Now I'm guessing your book might say 本を読むのを
やめた. ( not 本を読むのを
はじめた。)