Some tips and tricks to survive "in the hulk":
-prefer ranged combat. The ultramarines excel in that and are easier to play
-avoid melee as much as possible. The Genies are much better in that and can swarm you easily
-use overwatch a lot. The game is basically about covering different angles and slowly move your team forward.
-for most missions keep your team together and do not split them up. Keeping them together allows you to cover all threat angles much better.
-The first few missions are tough but as soon as your termies level up a bit it gets easier
-If you play one of the easier difficulties don't be afraid to loose a termie or two in a mission because they get replaced with equal termies after the mission. This way you can sacrifice one or two to save the others. Obviously that should only be done near the end of the mission.

There are a lot more guides and tutorials here and on Youtube.
I also recommend the "Cold Corridor Combat" mod since it adds more variety, bug fixes and better balancing.

When I first began playing the game, I was having serious issues with the first mission. Guns kept jamming, and as a result, melee would ensue and the Dark Angels would be slaughtered.

REMEMEBR to use that little X like icon in the bottom left of the screen, just above and to the right of the gun, when you have your soldier selected. It will cool your gun off and reduce the chance of it jamming.

Of course, overwatch is a must. The first mission of the Dark Angels, both squads can unload into a corridor that is PERFECT for overwatch use with their backs to each other. Never even need to move to finish the stage, just cool the guns, overwatch and end turn.