I believe that you'll be happier with the 3DS family of console over the DS/i family as the 3DS family is 99.7% backwards compatible with all DS/i games. I have to deduct 0.3% because of the Guitar Hero: On Tour series, which it's Guitar Grip add-on is specifically designed to fit the DS Lite ONLY.
By going with the 3DS family, you'll have the combined libraries (both the DS/i & 3DS + digital) to enjoy. You will likely want to go either with the New 3DS OR the upcoming New 2DS (available July 28, 2017), depending if autostereoscopic 3D visuals are your thing or not, for maximum library offerings as only the New 2DS / 3DS will support SNES VC titles as well as a few games that need the extra horsepower to run (all other games will just get a minor performance boost).
The only 2 reasons I can fathom that you'll need a DS Lite would be...
A) To play the Guitar Hero: On Tour series (as mentioned above, the guitar grip is specifically designed for that system)
B) To utilize a DS Flash Card... which treads into software piracy, as the latest 3DS firmware tends to block those.