The oak plywood at the borg is generally red oak. You can find a stain
color that looks good on that and then try to match it on the white oak
by mixing in a little bit of stain with a red tint to it (e.g. cherry).
It'll take a little experimentation.
The Hardwood Store (happens to be near me) has white oak plywood.
Since you claim to be a newbie, here's another piece of advice: oak is
VERY porous. Be very careful when gluing, as any glue which gets on
the wood will be absorbed into the pores and will block the stain from
absorbing. If you can, stain the individual pieces before gluing.
Otherwise, be extra careful to immediately clean up any glue drips with
a damp cloth or sponge.