Payday 2 DLC's

Weapon Pack 1 and courier.

Armored Transport, it includes new heists.

Weapon Pack #01 & #02 are good. Don't buy the Gage Sniper pack, I don't think it's very usefull unless you want the achievements (same for Courier).
And for Armored Transport, as aeternitas said, you can still join a lobby.

Mod Courier is actually the only one you (more or less) really need. The weapon packs are nice to have but thats it and you can play the heists without owning them.

Courier and Sniper

I'd get the Sniper and Mod ones. The sniper one is very useful if you will play high level missions, since it has a sniper that can kill shields with one hit and dozers with two. The mod one is simply useful for everything.

i would rate the DLCs as follows:

• weapon pack 1 (very useful weapons, grenades (beware of friendly fire))
• courier mod
• armored transport
• weapon pack 2 (weapons for higher levels/difficulties)
• sniper pack (very high damage, triple kills, shoot through walls and shields, only for experienced players due to slow rate of fire)

Absolutely get the Courier DLC, the others are mostly preference with possibly the exception of Weapon pack 1 since it has the convenience of grenades