Can someone give me a short description and comparison of the different road cycling pedal / shoe systems?
First up, I'd strongly recommend switching to clipless pedals. I had the same discomfort issues you're describing with normal shoes and toeclips and find clipless pedal so much more comfortable and secure (therefore safer).

When comparing and evaluating clipless pedal systems, some of the more important attributes are:


Float - This is the property where the foot can swivel on the pedal while clipped in. Some pedals allow the float to be adjusted independently of the tightness, while other pedals have only a single adjustment for both. Also, see this answer.
Ease of entry - Some pedals require the pedal and cleat to be lined up carefully before the cleat can clip in. Others are orientation agnostic and a good stomp is usually enough to engage the cleat.
Compatibility with shoes - Most shoes have either the 2 bolt SPD pattern (typically mountain bike and more casual style shoes) or the 3 bolt SPD-SL pattern (typically lighter and more stripped down road shoes)
Availability - How easy it is to buy parts, cleats and pedals.
Surface area - The size of the contact point on the shoe. This can make a difference in how evenly the pressure of the pedal is distributed to the foot.
Walkability - How easy it is to walk while wearing the shoe with the cleat.


These attributes for a number of different brands are compared in the table below.


Shimano SPD

The most common style of commuter and mountain bike pedals.

 

Shimano SPD-SL

The most common form of road bike pedals



Look Keo

The first popular road bike clipless pedal.



Speedplay

The speedplay pedal is becoming more popular with many professional riders now using it. One advantage is that there are no moving or wearable parts on the pedal, providing exceptional durability.



Time Atac

The Time Atac is another mountain bike style pedal



Time equipe

Time equipe is the road shoe style Time pedals



Crank Bros Eggbeaters

Crank Bros Eggbeaters are commonly used on mountain bikes where their simple design is good at shedding mud. There is some question about the durability of the bearings, however replacement kits are available, making these pedals more repairable.