I know. The subject is a mess but as a typography noob, I just didn't know how else to word my issue. Perhaps an image would be better.

I need the entire alphabet visually aligned within the orange box above. This font, as with many others, does not align with a text box, which then requirs manual nudging.
I'm building a website that utilizes a user's input text (e.g. "h") that would impose on this design. The problem is that because the letters all align differently, it is causing a terrible output.
My question (to this fine typophile community): Is there some setting or attribute about a font I should look for to achieve what I am after? Are my hopes and dreams about automatic visual alignment simply that; hopes and dreams?