Shimano SPDs sound like they would be a good choice for you. Not sure what's available in that range now, though I'm sure you could find something pretty cheap. Shimano also make shoes I believe, though you could also look at other manufacturers. Clipless pedals really make a difference. One of the most worthwhile things to do to improve your speed (and fun).
I don't have a bell/chime on my bike because, damn, it might weigh 100 grams!
Same with reflectors on the wheels, etc. I holler if an accident is about to occur, otherwise I just swerve and scare myself.
I don't know what kind of rims your bike has, but you could probably fit narrower tyres. But to be honest, the advantages of narrow tyres are often exaggerated. The main reason a road bike is faster than other bikes is because it enforces an aerodynamic riding position. At 30 km/hr on a flat road, about 85% of your pedalling effort is used to push the air out of the way. About 70% of that 85% is due to your body's drag, with the remaining 30% coming from your bicycle (these figures are for a rider in a low position on a road bike: on your bike your body will cause greater than 70% of the total drag). Narrow tyres have significantly less air resistance than fat ones, but because of these ratios of body-to-bicycle drag, you won't see a huge improvement by changing them. As for friction with the road, that forms only a very small part of your overall resistance (if the tyres are pumped up to the maximum allowed), and fatter tyres (smooth ones) actually offer marginally
lower rolling resistance than the ultra-narrow ones found on road bikes. They also offer better grip and comfort.
In short, the reason road bikes have ultra-narrow tyres is to reduce air resistance (and weight, to a lesser extent). But if you're sitting up in a non-aerodynamic position due to the bike you have, you won't see much gain by adding aerodynamic tyres.