Bench is great. Probably best not to do it the same day as overhead.
My program is structured around the compound movements forming the Cartesian product of {horizontal, vertical, leg} × {push, pull}; bench press is a horizontal push in this arena. Overhead press would be a vertical push, and squat would be a leg push.
Please don't spread out incorrect fitness advice, as it can lead to injury.
Disclaimer: I'm not a fitness expert either, just train regularly. So, verify anything I (or anyone else) tells you.
They work different muscles.
OHP/MP mainly works the delt, while the BP targets vrious parts of the pecs (depending on incline). Also grip width can change the balance between triceps/pec activation during BP
OHP gains certainly do carry over to bench press though. You can treat bench press as a "heavy" day lift and then use overhead press as a lighter pressing variation (but still go heavy) because there's enough overlap that it'll help your bench but different enough to where going heavy on overhead doesn't impact your bench press recovery.
Example:
Monday: 5 sets 5 reps of bench press.
Wednesday: 3 sets 5 reps of overhead press.
Friday: 1 set 5 reps bench press (trying to get as many reps as you can with good form, and increase the weight for next week depending on how many reps you went past 5)
Another way I've seen it done is something like this A B style workout:
Week A:
Monday - bench
Wednesday - OHP
Friday - bench
Week B:
Monday - OHP
Wednesday - bench
Friday - OHP
One really good source of info for powerlfiting / strength programming on youtube is Alex Bromely
My program is structured around the compound movements forming the Cartesian product of {horizontal, vertical, leg} × {push, pull}; bench press is a horizontal push in this arena. Overhead press would be a vertical push, and squat would be a leg push.