Whether you are on a professional or a personal shoot, there are positions you should never shoot without. On a small budget you may find people doubling up on jobs but here's the positions that I find to be the most crucial (other than a writer/director/producer).
1) Sound Mixer
This is the most important person to have on the list. Having some one dedicated to sound can ensure that you will end up with at least decent sound. Sound Mixers will often say that sound is 50% of your movie. And if you only have a small crew, this is the first person you should find. Even a friend holding an H1 on a monopod is better than nothing.
2) Director of Photography
Many directors like to operate camera but getting some one else to think about the look allows you more time to focus on actors. The director of photography will also help think of creative ways to shoot the scene and often be crucial to the schedule (so be sure they can work at a decent pace). This is also a great person to have if you don't a good camera or just want to up the look of your film.
3) 1st AC/Gaffer
An assistant camera will ensure that your footage is in focus. He can also help your DP setup lights and just in general speed up the film.
Honorable Mention - Production Designer
Without a Production Designer, all of the Art falls to the director. On a simple film this may not be too bad, however the larger the film the more important the Production Designer is.
Zachary Will is an Award-Winning Filmmaker creating short films and content for the Internet as the owner of Riverside Studios. He has a Bachelor's in Film from Full Sail University. He has worked on productions for companies like Webmd, Sears, Home Depot, Six Flags and more!
"the trick is to never give up... I think the secret of success is not how little you get knocked down but how often you get back up." - Gareth Edwards