Because of a certain 140 character limit I've learned where I can trim characters on responses but even after all this time I still reply with "Well, so and so . . ." and I go back and have to delete it (even on comments to this site I start with well and then delete it). Is it because that's generally how I would speak a response and I should watch out there too or is this just me?
Well, it is a context marker, showing that you are launching a story. Examples of context:
"Did you do your homework today?", "Yes" is an acknowledgment of dialog.
"Did you do your homework today?", "Well, yes" means you want to shift to a story.
"Did you do your homework today?", "Uh, yes", another context marker, means that your answer is unofficial, off-the-record, or unverifiable.
"Well" is not necessarily a needless word. It's a discourse marker. Wikipedia on discourse markers.
It's kind of funny to see you asking us what you are thinking.
My guess would be that you keep doing it because you innately feel like that word actually does impart some important information.
My second guess would be that the information in question is something along the lines of "The words that follow are just musings off the top of my head on the issue you (the other party to which you are responding) just brought up." Without the "Well" it could be taken as some kind of prepared or dogmatic statement, and/or might not nessecarily relate in any way to the previous statement you actually want it related to.