There's a lot of debate over whether clipless makes you no faster or a little faster (some studies have shown no improvement, but they're testing indoors) and most of the point of clipless other than fashion is just in keeping your foot attached to the pedal.

I know I went through several pairs of clipless shoes, pedals, and ended up back at wearing good regular shoes with good regular pedals.

Just fyi.

For your other questions, it's a lot cheaper usually to buy pedals and cleats online, but I'd always buy shoes either in person where I could try them on, or through somewhere that lets me ship them back as shoes need to fit.