There are a variety of ways to do this but the biggest obstacle is that QuickBase was not designed to be skinnable so you might achieve setting the font in one area of the application that looks nice but the changes could bleed into other areas of the application where it does not look so nice. Thus you will probably have to do a lot of experimentation with settings no matter what road you go down.
I would start with Chrome and load this extension:
Attached is a screenshot of setting the font to Arial 18pt using Font Changer:
If you think Font Changer can make the page look acceptable for your needs you could then pursue a script solution that could make the changes in just specific areas. I would not jump into a script solution immediately as you need to do a lot of experimentation on a fast cycle. There is no doubt script can do this but the main obstacle is that QuickBase was simply not designed to be skinnable and you will constantly be tying to override their CSS in just specific areas.
BTW, here are the settings I used for Font Changer: