A sturdy vessel is also needed for water purification. While this is a subject we've covered thoroughly, please consult those articles as you consider what kind of bottle to choose.
The first metric I consider in a water bottle is the material it's made from. Plastic bottles are cheap and common, and work great for things like trips to the gym and days at work, but their big weakness is that they don't hold up to high heat well. This is important when you try to boil water to purify it! With that in mind, any bottle that I may need to cook or pasteurize in is made of stainless steel and is single-walled (see below). I still have and use a plethora of plastic bottles around the house, but they're not in my camping/bug-out gear or in my EDC pack.
Bottles are available in single-wall (not insulated) and double-wall (insulated) varieties. Double wall bottles are awesome at keeping hot things hot and cold things cold. I carry a double wall bottle to work, so that my summertime water is cooler and I can keep tea or cider hot in the coldest Utah winters. However, that same insulation keeps me from heating water in the bottle. Single-wall bottles don't insulate worth a darn, but they allow the contents to be heated readily.
Single-wall stainless bottles are still available in a variety of pretty colors and designs. Coatings can react poorly with heat, though, possibly releasing toxic fumes. With that in mind, look for a plain stainless bottle for your purifying needs.
I like my bottles between 20-32 oz, with a personal preference for larger bottles when I have a choice. Below 20 oz, you're not carrying enough water to be useful; above 32 oz, you're packing quite a bit of weight and bulk. I also am a fan of wide mouths, because I find them personally easier to fill and use, especially if you want to add ice cubes to your drink. Two very good examples are commonly available, and Kleen Kanteen also offers 40 and 64 oz versions, if you have particular need for them.
If you don't want a bottle you can heat in (and there are many perfectly valid reasons why not), your alternative is a small pot. I carry this in my Bug-Out/camping pack. Pots like this weigh virtually nothing, hold a useful amount of water, and allow for the easy use of a WAPI.
No matter what vessel you choose, water is critical to life, and you should always have a way to carry safe drinking water handy. Determine your needs, then fill them appropriately.