A higher-speed film may extend your flash by a few feet, so it does pay to use the higher-speed film, even indoors for flash pictures.
A dim-light film (also known as fast or high-speed film) is extra sensitive to light so you can get good pictures in very dim light. Use a film rated at 400.
KODAK High Definition 400 Film is designed for exposure with daylight or electronic flash; you can also obtain pleasing results under most existing-light conditions.
From Kodak site
KODAK High Definition 400
http://www.kodak.com/global/en/consumer/products/techInfo/e7013/e7013.shtml#existing light
Existing Light
Subject and Lighting Conditions
Shutter Speed
Lens Opening
Home Interiors at Night
Average Light
Bright Light
1/30
1/30
f/2.8
f/2.8
Aerial Fireworks
Bulb[1]
f/4
Interiors with Bright Fluorescent Light
1/60[2]
f/4
Brightly Lighted Street Scenes at Night
1/60
f/2.8
Neon and Other Lighted Signs
1/125
f/2.8
Floodlighted Buildings, Fountains, Monuments
1/60
f/2
Night Football, Soccer, Baseball, Racetracks
1/125
f/2.8
Basketball, Hockey, Bowling
1/125
f/2
Stage Shows
Average Light
Bright Light
1/15[1]
1/15[1]
f/2.8
f/2.8
Circuses
Floodlighted Acts
Spotlighted Acts
1/125
1/250
f/2.8
f/2.8
Ice Shows
Floodlighted Acts
Spotlighted Acts
1/125
1/250
f/2.8
f/2.8
School
Stage and Auditorium
1/30
f/2
[1] Use a tripod or other firm camera support for exposure times longer than 1/30 second.
[2] Use shutter speeds of 1/60 second or longer with fluorescent light.
