Quite likely to be pitch pine. So-called because the tree oozes pitch that was used to waterproof boats etc.
Stain would alter the colour, so I guess you wouldn't want that. The two ways that I like are...
Beeswax, or even furniture wax. Used on stripped pine doors. Applied with a soft cloth, fine wire wool. The wool helps smooth the raised grain in the timber.
Oil - any kind of "Finishing Oil", "Danish Oil", or "Teak Oil". Apply sparingly with a cloth. Rub in well, and build up with more coats if you like. Don't apply with a brush. Oil dries slowly. A brush puts too much on. The top surface dries, but leaves a thickness underneath that makes a sticky mess.
Experiment on a small area first with oil. Remember that wax will cover oil, but not the other way around.