You could do it like Del says, or you could start from the beginning, like I did, and let me tell you, it really gives you a nice sense of progression throughout the series and lets you appreciate the little things. If you do start from another game, just keep in min that I, II and III have to be played in order to fully appreciate, and the same goes for IV, V and VI, as while the series as a whole is pretty much like FF in that they're all separate stories with separate worlds, these two trilogies actually have games that form a much deeper connection even in story, especially the first trilogy.
The first three games are available on mobile (and if you decide to emulate them instead, go for the SNES versions), while IV, V and VI are available there as well, and in DS. VII and VIII are on 3DS (VIII coming out in January, unless you go with the PS2 original), while IX is on DS. X still hasn't released outside of Japan, but the chances are growing, judging by the release of VII and VIII on 3DS and the fact that China is getting the game.
Check out my reviews for I-VI if you're interestedIf anything, DQI is at least a very short game, so you can always check that out. It's worth taking a look just to see what the first ever JRPG was like.