Catra, reusing disposable plastic water bottles is not advised. The plastic starts to break down and chemicals can leech into your water. Pur (Brita likely has a version as well) has a travel size water bottle with a small filter in it. They're plastic as well, but higher grade that's supposedly safe.

Different bottled water has different levels of trace minerals, and the different filtering (or lack there of) process can definitely change tastes as well. Some bottled water is simply tap water that goes through a filtration process. Fiji water has a high silica content, so it's very smooth. I used to be a bottled water snob. Voss is my favorite hands down. It's also remarkable the difference in taste of tap water depending on location. I moved last year, from an area where there were reasons to be concerned about the water, and it really is nice to no longer have to deal with trying to transport heavy water packs with one hand!