Order parameter and Bose-Einstein condensation

I mean the two main textbooks for this are:

• Pethic & Smith, Bose Einstein condensation in dilute gases

• Stringary & Pitaevski, Bose Einstein condensation (and Superfluidity)

which cover both the theory and the experimental stuff.

Otherwise, any lecture notes online cover the basics of BEC.

As a quick answer to the key words in your title/question:

• The order parameter is usually chosen as the population in the ground state $|Psi_0|^2$ which is $sim 0$ for $T>T_c$ and $underbrace{neq}_{text{macroscopically}} 0$ for $T<T_c$ and $1$ at $T=0$.

• The symmetry broken is $U(1)$, since the BEC is a single mega-wavefunction with just one phase. The choice of a single phase breaks the $U(1)$ (the group of phase factors) symmetry of the thermal state.