Mark from migrationology has a good guide on apartments in Bangkok. It’s a bit dated but in principle still spot on.
As to the area, it depends on you and you alone. Expats and also many DNs seem to like the Sukhumvit and Silom areas (aka New Bangkok). That’s where the Coworking spaces, shopping malls and fancy restaurants and hotels are. It’s also where the Skytrain runs.
But Sukhumvit and Silom are pretty much your run-of-the-mill Asian skyscraper megacity. It’s where the business is, but as a DN you don’t have to care about that.
There’s not much of Bangkok’s charm in New Bangkok and the prices are sky high compared to other parts of town.
That’s why I prefer Bangkok’s Old town (Phra Nakhon) to stay, especially Banglamphu and even more so Sam Sen area: No skyscrapers, wooden buildings, relaxed atmosphere, temples, parks, close to the river (and the river express boat), Jazz Bars and the tourist district for nightlife.
Thonburi on the other side of the river is even more laid back and “Bangkoky”, but transport options are much worse than in Phra Nakhon.