My boyfriend and I are new too! We've been playing for about a month. I suggest you play combat training, team death match, start on recruit level. You'll be paying with and against AI characters, not real people (although xbox may use your friends names for th AI characters). You'll still die like mad at first, but you'll get comfortable fast. It's given us a chance to learn the maps, weapons, perks etc. and how the game is played. We've learned so much doing this, and I HIGHLY recommend it.
When I was new to the game, I had the same problem. Now I'm Rank 14, Prestige 1 and I have game play videos of me and my friends playing on YouTube. Anyway, to start off, Free For All isn't always the best idea, since you're by yourself. I would start on Team Deathmatch, watch killcams of the other team, and watch your teammates for some tips and tricks to improve. Don't start off using a LMG. Not only will you be called a "noob" constantly, it won't help you with your aiming/shooting skills down the road. A MTAR is probably the best, and already unlocked from the start, weapon you can go with at first. (It's an assault rifle btw.) I used it, kept upgrading it, and found that the Target Finder was the best for getting quick killstreaks and learning how to get a better K/D ratio.
My advice for not getting killed.. put some grip tabs on your analog sticks and turn the sensitivity up to high (I usually keep mine at 7). This allows you to make better/faster turns and aim better, thus enabling you to see around you better and not get killed.
I hope this helped somehow