Really... I don't think you can get enough water out of a counter top model and it surely couldn't store much.
I would recommend you install an under the counter model with a spigot next to the faucets in your kitchen (this is what I did). I got a 9 gallon per day model fo my family of 5 (which as it turns out is a little small... we run out of Reverse Osmosis (RO) water during peak demands. I bought from www.freedrinkingwater.com which is a reliable and good company (no affiliation). I also got the Ultra-Violet (UV) sterilizer feature that kills spores, cysts, virii, etc. The water provide water to my refrigerator for ice and the front door has a cold water dispenser too. You can also get a unit from your local Home Depot/Lowes (hardware store). Easy to install.
In my home we believe that tap water is effectively "poisonous"... we take showers with it and flush the toilet with it and do our wash with it but NONE of it goes into our bodies. Even boiling potatoes or making pasta we use RO water. I recommend EVERYONE do it for their health and the health of their families. The FDA allows a threshold amount of toxins in the water and from time to time the thresholds are exceeded but the truth is that every single molecule of toxin has some negative effect in your body... maybe unmeasureable but could manifest itself as lukemia, cancer, MS, or something one day after years of daily "assaults".