In most of my initial plays through a new Gen, I mainly keep a balanced team of Pokemon with various types: Fire, Rock/Ground/Steel, Electric, Grass, Water, and Psychic/Ghost/Fairy. I've learned to simply keep a few Pokemon as HM slaves and just swap it with one of my party members (as it makes for a more challenging play).
With remakes, however, I tend to plan ahead and create a party based on the challenges that I will face in the Main Story.
For instance, in Omega Ruby, there is a lot of water to traverse and explore in, so my party consists of Pokemon who can learn such aquatic maneuvers (i.e. Surf, Waterfall, and Dive).
Here's my team:
Blazekin - Blazekinite
Groudon - Red Orb
Magnetzone - Magnet
Ludicolo - Miracle Seed
Sharkpedo - Mystic Water
Dusclops (hoping to evolve to a Dusknoir soon!) - Evolite (then Expert Belt)
I have to admit that after Gen 6 introduced Fairy-types, Steel-types have become a lot cooler.