Bottled ink is one of the joys conferred by fountain pen ownership. An enormous range of colours are available (you can even mix your own); it can be economical and eco-friendly; and there's some satisfaction in the process of filling a pen.
It can of course be inconvenient at times, but the sheer variety of ink on sale in the 21st century is a testament to the ongoing popularity of bottled ink and the affection in which it is held.
Any fountain pen can use any reputable brand of ink - despite what pen manufacturers and their vested interests might imply. It's true that there are some pens that are more fussy about ink than others, and there is quite a wide variation in the viscosity and colour of the various brands, but in general the choice of ink will normally come down to personal preference or cost.
However, two brands which stand out in most often in polls of fountain pen users are Waterman Ink and Diamine Ink, and we heartily recommend these to any fountain pen owner. Diamine in particular offers an enormous range of colours and it's still manufactured right here in the UK. We love their inks so much that we've had them make a small range of extra colours especially for us - see our Cult Pens Deep Dark Inks.
Fountain pen ink is not generally very waterproof - the properties that make ink waterproof are not friendly to delicate fountain pen innards. However, Platinum's Carbon Ink is about as safe as it gets and is thoroughly waterproof. You'll need to rinse out your pen before storage though. Graf von Faber-Castell's line of luxury ink is safe for any pen, and boasts impressive if not bullet-proof tolerance to water.
Finally, if you fancy creating your own unique ink colour, try Platinum's Mix-Free Ink - colours specifically designed to blend with each other.
For an excellent overview of fountain pen inks see Rick Conner's article here.