Let's get a few things straight here...
(GBA) Advance Wars
(GBA) Advance Wars 2 (might as well have been Advance Wars 1.5)
(NDS) Advance Wars Dual Strike (AKA Advance Wars 3 for NDS)
(NDS) Advance Wars Days of Ruin (could be loosely considered Advance Wars 4, but it's different enough in story, unit types, unit abilities, and COs that it's a stand alone Advance Wars)
All that being said, I'd say if you're playing GBA, get Advance Wars 2. If you're playing NDS, either Dual Strike or Days of Ruin are good choices. If you were to never have played either and saw each of them played side-by-side, I'd say your decision might boil down to personal taste of the themes. I personally prefer DoR for it's darker theme and exceedingly better soundtrack. I'll never say that DS or DoR is overall better than the other. They are equally superb games, each with their own pros and cons. Obviously, the addition of NintendoWiFi battles sets DoR ahead of DS, but only for that reason. Saying DoR is a better game for only that reason is hardly fair to Dual Strike, which offsets DoR with more content.
You're missing about half the series. It first debuted as Famicom Wars on the Famicom, there's a partial translation patch if you ever felt like picking it up. It does not work in PocketNES/NESDS--unsupported mappers or whatever.
They made a sequel, appropriately titled Gameboy Wars. Take a guess which system.
They made three others. Gameboy Wars Turbo on the Gameboy, GB Wars 2 and GB Wars 3 on the GBC.
Somewhere in between there they released Super Famicom Wars.
They're all pretty much the same exact game, so that makes Advance Wars something like System Wars v7. AW2 System Wars v7.5? Who can even count after all these years?