Step 1: Examine each statement.
\[
\begin{aligned}
I. &\text{True} &&\text{Sarcoplasmic reticulum stores Ca}^{2+}\text{ ions.}
II. &\text{False} &&\text{Thin filament contains actin, troponin and tropomyosin, not myosin.}
III. &\text{True} &&\text{Thick filaments are held together by the M-line.}
IV. &\text{False} &&\text{Sarcomere extends between two successive Z-lines.}
\end{aligned}
\]
Step 2: Identify the correct statements.
\[
\boxed{\text{I and III}}
\]
Step 3: Choose the correct option.
Hence,
\[
\boxed{(A)}
\]
is the correct answer.