The best FF games are FF VII and FF VIII, my personal favourite. Other FF games widely recognized as really outstanding games are FF IX, FF X (although I personally found it a tad dull), FF VI and FF IV. A good game to start, I suppose, could be FF VII, because it was the first 3D Final Fantasy game and it also boosted the popularity of the series an awful lot. However, you can only get that on PS1 or an illegal copy on you PC :laugh:
So, if you want something that you can play with either DS or PSP, I recommend getting FF IV for DS. The first Final Fantasy games were super hard and had no storyline, so I don't recommend getting them. FF III is pretty good, but also very hard.
It's really up to you. Go to some place with reviews (IGN or someone of the like) and check out what kind of reviews each one has gotten. Then, by those reviews, you can pick the one that suits you most. If you ask us, we'll just keep giving you our opinions, and that might not really help at all. For example, I love FF VIII, but it's not everyone's cup of tea. You should get to know something about those games and decide after that.