By the definition it looks like 'Every solvable primitive groups are of affine type primitive groups only.' Is the converse true ? i.e. Is it true that every affine primitive permutation groups are solvable ? If not true, 1. is there any counter example. 2. What is the bound on the base size of primitive groups ?
Note: It is known that every solvable primitive permutation group has base size bounded by 4 [AKOS SERESS, 1996].
Please refer a text 'Permutation groups' by Dixon and Mortimer for standard definition such as primitive groups, permutation groups, Classification of Primitive groups.
The largest affine-type primitive groups are the groups ${\rm AGL}(d,p)$, which have the structure $N \rtimes {\rm GL}(d,p)$, where $N$ is the translation subgroup of order $p^d$. These are not solvable for $d>1$ (except for $d=2$, $p=2,3$).
For primitive but not $2$-transitive groups of degree $n$ there is a base of size at most $4 \sqrt{n}\log n$ (Theorem 5.3A of Dixon and Mortimer), and for $2$-transitive groups that do not contain $A_n$, there is one of size at most $72(\log n)^2$ (Theorem 5.6A of Dixon and Mortimer). These bounds are not sharp but they are of the correct order of magnitude.