I'm reading into classifying spaces for the moment and I have some questions about these things. I'm using the following definition:

Given a group $G$, a classifying space $EG$ for this group is a $G$-CW-complex that is contractible.

These spaces seem to exist and be unique up to $G$-homotopy for any group. I was wondering if there are criteria such that if these are satisfied by $G$, then the $G$-CW-complex $EG$ is finite (or, more general, of finite type)?

I do not immediatly find an obvious answer. For example to ask that $EG$ is finite already fails when taking $G$ to be finite. i.e. $\mathbb{Z}_2$ has $E\mathbb{Z}_2$ the infinite sphere $S^{\infty}$.

If someone could recommend additional literature on classifying spaces, please do. This will be highly appreciated!

Note: this question was edited after a comment below

I'm reading into classifying spaces for the moment and I have some questions about these things. I'm using the following definition:

Given a group $G$, define the total space $EG$ for this group to be a $G$-CW-complex that is contractible. Next we define $BG=EG/G$ to be the classifying space of $G$.

These spaces seem to exist and be unique up to $G$-homotopy for any group. I was wondering if there are criteria such that if these are satisfied by $G$, then the CW-complex $BG$ is finite (or, more general, of finite type)?

I do not immediatly find an obvious answer. For example to ask that $BG$ is finite already fails when taking $G$ to be finite. i.e. $\mathbb{Z}_2$ has $B\mathbb{Z}_2$ the infinite projective space $\mathbb{R}P^{\infty}$, which has one cell in each dimension.

If someone could recommend additional literature on classifying spaces, please do. This will be highly appreciated!