What do your contacts say at the major airlines, the ones that are going to help you get hired? If you don't have these, it's probably going to be pretty tough to get hired without 121 currency and experience. The type, while probably fun, won't really help much and you'll get a type at a regional no matter what, exactly which one won't matter that much to the major airline, they just want to see you are trainable so they won't be wasting their time giving you a type ride. Many pilots consider a type rating without experience to be a detriment to hiring, but I doubt HR departments really think into it as much as pilots do.