A few responses:
1. Landscape vs Portrait with 300: Personally, I shoot 90% of baseball in landscape with the 300 and then as and if needed, will crop into portrait mode (see first photo below for example). A time when I do shoot portrait is when I am close to pitchers, or from behind the plate and want to get a full body shot (see second below for example):


2. Your baserunner image: The shot is overexposed to begin with and also looks out of focus a bit. I don't have an EXIF reader, so don't know what your settings were, but my base settings for baseball are Av mode with Aperture of 3.2-4.0 (depending on how much DOF I feel like for the day) and then a shutter speed of no less than 1/1000 and then adjust ISO as needed to get there. On sunny days like this, I will also overexpose (EV + 1/3 to 2/3) to lighten shadows under caps and such. Use the center point only for focusing, AI Servo mode, and try and learn how to use the back * button for starting the AF. Also shoot RAW and then after editing export to JPEG. Way more latitude with editing light issues with RAW images, than there is with JPEG.
3. The post above asks Why 1600 ISO?: As noted above, I like to keep shutter speeds for baseball at 1/1000 and often way higher. Obviously on bright sunny days I can get away with 400-800, but as night falls and on overcast days, sometimes 1600 ISO or higher is needed to stay there. In fact the pitcher photo above for example was at 2500 ISO.
4. Lightroom and Post Processing - I use LR for pretty much 99.99% of my processing and workflow...import, select, edit, crop, rotate, export to JPEG. It is a fantastic tool and well worth the investment. It also has great noise reduction and allows me to get useable sports images at 6400-10,000 ISO and higher. I agree with D. Warren above, and feel that taking the picture and getting your settings right in camera is about 25% of the job, properly post-processing it (adjust lighting as needed, fix shadows and highlights, crop, straighten, etc) is the other 75%.