Nintendo DS, shooters, GBA & TV connection…

[ST Dragon]

Hello,
I’m interested in buying a Nintendo DS so that I can play the shooters available for it, the older GBA games and also be able to hook it up to a regular CRT TV via composite RCA, using one of those 3rd party wire adaptors I’ve seen in various shops.
I’m not sure if this is even possible on an older CRT TV via composite RCA or only on a digital TFT/LCD TV, as it has newer HDMI input.

At my local game store there are 3 Nintendo DS types:
1.Ninntendo DS Lite (2006)
2.Nintendo DS Lite (2008)
3.Nintendo DSi (With A camera) (2009)

So, which of the 3 would be the best choice for all my expectations?

Thanks in advance.

[lgb]

The DSi has no GBA slot.