Arranging the given signs and symptoms in the increasing order of their appearance in pregnancy:
\begin{itemize}
\item Palmer’s sign (B): This refers to regular painless uterine contractions felt by the examiner on bimanual examination and typically occurs between 4 and 8 weeks of gestation.
\item Hegar’s sign (C): This is a softening of the lower uterine segment (isthmus) that can be detected on bimanual examination, usually occurring around 6 to 12 weeks of gestation.
\item Quickening (A): This is the first perception of fetal movement by the mother, typically felt between 16 and 20 weeks of gestation (earlier in multiparous women).
\item Lightening (D): This is the sensation that the fetus has "dropped" lower into the pelvis, relieving pressure on the diaphragm and stomach. It usually occurs a few weeks before labor in primigravid women (around 36-38 weeks) and may not occur until labor begins in multiparous women.
\end{itemize}
Therefore, the correct order of appearance, from first to last, is Palmer’s sign (B), Hegar’s sign (C), Quickening (A), and Lightening (D).