You've heard lots of very good - and sometimes conflicting - advice and points of view, as is normal in such a diverse community.
The life of many creative endeavors is very solitary - writers, painters, composers and the like. Bands are very small closed structures similar to a family. Filmmaking is entirely different; it is almost impossible to do everything yourself, and not even recommended that you DIY even 20%. This is why you need creative partners. An active line producer at the big-budget level is your buffer between and your communications with the "real" world; your 1st AD is your buffer between and your communications with cast and crew. Even though my descriptions are very similar they are entirely different jobs. The line producer protects you from wasted time, allowing you to be the creative artist; the 1st AD streamlines your interactions with the creative crafts and the talent, allowing you to be the creative artist - subtle but important differences.
At the low/no/micro budget indie level the two jobs - line producer and 1st AD - are combined if it exists at all. Don't worry too much about the label, but it is always a very good idea to have another person who is totally committed to you as a director and committed to your project. You can call him/her a producer, 1st AD or anything else that you or s/he wants. The important thing is that you have a common creative vision and an easily flowing communicative rapport. You bounce ideas off of each other, encourage each other when one of you is down, celebrate together when things go well, and shepherd your flock (crew and talent) towards the finish line of a good project. So put aside definitions and try to find a creative partner.