Yep, that's basically it. Though you do need to find the proper firmware for your particular flashcart, and I would avoid anything with the R4 name on it.
Also, the DSi blocks out most flashcarts. You need one of the newer generation ones for that, such as the M3i Zero or the Acekard2i.
As for which is better, that's up to you. The DSlite has better battery life and the ability to play GBA games. The DSi has less battery life and can't play GBA games, but it can browse the net and download DSware games from nintendo. So it's your choice what you want.
AS above R4 when it comes to flashcarts is like a household name everybody who's looked into modding if they only know one thing is R4, little info is deadly lol they don't know how bad R4's have got recently. basically lack of updates to play new games. most flash carts can be upgraded to 1.4 now even things like dstti
Get a DSi. The lack of a GBA slot is nothing to worry about, because the iPlayer can play GBA games. It can't play commercial DSroms though, as it is primarily made for watching films. Also, there'll soon be a SuperCard DSTWO, which will allow for both playing GBA and DS games AND watching films. I suggest you wait a little bit until it's out, then order one.
If this post is hard to understand for you, I'll try and explain it better.
