I would go one day bench press and one day weighted pullups or chinups OR bench press one day and db bench press day 2.
It seems I'm a little late to the party here, I don't post much because I prefer to learn from those that know more than I do, (I walked on to my colleges track team, didnt run in hs) but before I blew up my arm (playing bball in hs) I was a DI baseball recruit as an outfielder, I do know baseball like the back of my hand though.
Speed is at a premium in baseball especially college there just aren't many good american athletes playing baseball. Sprint training with a football like lower body lifting regiment (Defrancos) helps for speed development just as much because baseball tests the 60 yard dash. All you have to do is run under 7 seconds and coaches will like you, I usually ran a 6.7 and they were all over it. One of my friends ran a 6.5 and he was 6'5 he could've literally went anywhere to play.
You should NEVER barbell bench press, throwing puts enough stress/destruction on your shoulders you don't need to add to it by bench pressing. I benched for football in HS and I stopped after my sr yr football season and started doing more chinups and my velocity jumped about 7 mph. pushups and DB press are ok. You should do two sets of pull for every set of push.
And for the record baseball is the ultimate skill game. Why is it that there are so many kids from such a small place (Dominican Republic is just one example that comes to mind but just about anywhere in the Caribean can be used as an example) playing professionally? The fact is they play ball EVERY SINGLE DAY, here in america kids barely play AT ALL in the winter and play maybe 4 times a week (usually less) in the summer, also theses kids play the right way many former and current pros teach them the right fundamentals at an early age when most american players NEVER learn the right fundamentals.
Being a better athlete/ training to be a better athlete will help you in baseball because so much emphasis is put on your 60 time, but it will NOT make you a good hitter (Yes it will increase your potential bat speed, so you'll potentially have more power and with that potentially a better average) It can make you a better hitter, but if someone doesn't know the correct mechanics to throw/swing they will never be able to express their true bat speed no matter how much potential they have. (If Usain Bolt had shit running mechanics, he wouldn't be nearly as fast as he is). So SKILL always comes first especially for young players, a lot of those guys from the dominican (just one example i mentioned earlier) are not neccesarily strong or fast (middle infielders and outfielders are fast, but many 1B/3B are not) but they play the right way, every day, and with practice you do increase arm/bat speed. (Same with track- the more train the right way, the faster you get!)
Yeah, for whatever reason, 60 yard times in baseball are seemingly just as important as 40yd dash times are for receivers and D backs in football. Makes no sense at all to me. In my mind, college coaches should always take a better bat over a better athlete at most any position.
I saw a D1 centerfielder on a top 10 team that has no arm at all. He can't make a decent throw from shallow center. Yeah, he's fast, but....
Also, clocking kids on a straight 60 makes no sense. Either clock them on a straight home to first, or home to second..