。
Let's pick some out for mother.
Literal
Mother [to-に] those [obj-を] pick-out give (volitional).
The volitional form あげよう ('let's give / I'll give') + ~て form of 選ぶ ('pick out') chains into 選んであげよう = 'let's pick out and give' = 'let's pick out [for mother].' The benefactive ~てあげる adds the 'for someone else's benefit' direction that 選ぶ alone lacks. 選んで comes from 選ぶ, a godan verb that conjugates irregularly in the て-form: えらぶ → えらんで.