Architecture of speaker (drivers) to get an acceptable level with small dimensions
Enclosures make a huge difference to speaker loudness. The one in the iPhone is small, but you can bet it's optimized for clarity and loudness of middle-to-high frequency audio.

For your goals (bright + small) choose a driver with high efficiency at 1kHz and above. Aim for over 100 dB/W/m if you can.

If your enclosure size is fixed, then do what you must. Otherwise note that larger enclosures generally provide better low frequency response, and harder enclosure materials will help with high frequencies. Use a sealed (no holes or "ports") enclosure unless you want to learn all about Thiele-Small parameters. Sealed enclosures are easy to make and (more importantly for you) perform well for mid-to-high frequencies.

Lastly, the other key factor to obtaining a bright and loud sound is the power amplifier. Buy or build one that can put out at least as much wattage as the speaker's RMS rating. Sizing the amp is a matter of which device you'd rather start distorting first. Amplifier distortion might be pleasing to your ear (depending on context and the way the amplifier distorts), but speaker distortion rarely is.