Adding Circuits using ROMEX® vs. AC cable

My house was built using AC cable (w/bonding strip). I am now refinishing my basement and would like to add circuits from the fuse box using ROMEX®/NM....I have found working w/ROMEX® to be much easier/cheaper. Is this allowed code wise? If so how do I ground the ROMEX®/NM in the fuse box?
Sorry for the repost.

Where are you located?
Codes vary by area

tx for the reply..... I am in New Jersey..

NM cable should be fine unless you are in some big city. Even NYC relaxed it's "no NM" rule.

In the main panel the grounds go on the same bar as the neutrals. Do not connect both ground and neutral in the same hole.