DS Lite all the way. I'd say... buy the thing if it has any game that interests you, Proto. I've seen some pretty interesting games lately for the DS, and there are more to come.
RTS... there are some, but mainly extremely rare titles and most are not the kind you see on PC. But give TBS a chance. There are some pretty good gems on the DS if you can tolerate the presentation.
RPG... there are lots. We are talking about remakes of Final Fantasy games all the way up to IV now and Dragon Quest IX along with a whole slew of other stuffs. Square-Enix has been pretty active with this one, and trust me, it feels like the SNES all over again... Good ol' days. And that's just S-E. Sega also makes some Sonic RPGs (yeah... Sonic RPG for real), Nintendo has been milking Mario ever since Mario & Luigi, and there're the Pokemon games. Then you have Atlus and the rest of the gang, too. RPG on DS is a rich land.
Action Adventure... you have Zelda Phantom Hourglass for now and it should take you a couple of hours. The next Zelda game for DS will come out next year. After Zelda, I don't know if there is anything else, but hey, IMO, Zelda is enough reason.
If we're talking about point and click adventures, on the other hand, it depends on what you can savage from your local game stores since I don't think game stores stock too much of those. But... DS does have a lot of these games. And there are talks of developers remaking some point-and-click games for the DS.
As for gaming life, I believe DS will have another two years to go at the very very least. Nintendo just introduced DSi. They are obviously in no rush to "innovate" or "update" the DS seeing as to how it's already good as is. Typically, if nothing new has been announced by Nintendo, it'll stay that way for years until they actually announce something.
I have a PSP. And truth be told, I like my PSP more than my DS. But more truths be told, I play on my DS more than on my PSP. PSP feels like it's just there for the novelty. PSP games are nice, and honestly, I have a lot of them, and the average time I spend on a PSP game is enough for me to complete around 10 DS games or more, but... there are just so few titles on the PSP that interest me. Lack of developers' interests is really a crime in this case. Homebrews on PSP are nice, but aside from offering a decent web-browsing experience, or maybe some retro games, or maybe radio and stuffs, they don't do anything that my ultra-portable PC can't do. And the DS can also do a couple of those things. So as much as I like my PSP, my UMPC + DS combo takes the win, and I don't even think about PSP vs UMPC because both can't fit in my pocket, and if I have to lug around a backpack then I might as well lug around a UMPC instead of the PSP. Size is a concern there.
^= And to PSP GO naysayers, PSP GO actually "fits" into your pocket. I succumbed to one of them and I gotta say the darn thing feels pretty good compared to the original PSP. I'll see about a review at some point...