Newbie upgrade questions

Well, first off, the i3, i5, and i7 designation is just for marketing purposes on the part of Intel, so consumers have a quick way of determining what the different processors are capable of. Roughly:

i3: entry-level - cheap, best suited for light computing, like web browsing, office work, etc.
i5: mid-level - more powerful chips that are better for gaming, multi-tasking, hd media consumption
i7: enthusiast/professional-level - most powerful chips available meant for enthusiast gaming, heavy multi-tasking, or professional-grade productivity work (video editing, 2d/3d rendering)

The number that comes after the i3/5/7 is the model number of the CPU. In general higher number = newer and/or faster processor. The first (leftmost) digit usually indicates generation number, so an i5-2xxx is a second-generation i5 CPU (also known as Sandy Bridge), and an i5-3xxx would be a third-generation CPU (also known as Ivy Bridge). The other digits in the model number will tell you the quality/speed of the CPU within the generation that it belongs to, with higher numbers generally indicating faster CPUs. So an i5-2500 would be faster than an i5-2400.

As for power consumption, this really only matters when it comes to your power supply unit (PSU). The PSU supplies power to all your PC components, and can only deliver so much power (wattage). Thus when upgrading, you want to make sure your new CPU does not make your PC exceed the power capabilities of your PSU.

As for the T or K designations, 'K' means a CPU has an unlocked multiplier. This has to do with overclocking (increasing the clock frequency) of the CPU. So if you don't plan on doing any overclocking, you can ignore K chips. The 'T' letter simply marks a CPU as being energy efficient, which Intel defines as having a TDP (power requirement/wattage) lower than a certain value.

As for vendors, Newegg and Amazon are two very reliable retailers that I routinely use. They also supply user reviews for their products, which can be useful. This is another good site where you can browse through options for each computer component, and it will automatically look up retailers and the best price, as well as factor in sales, rebates, and shipping costs when applicable. I use it to find out which retailer is offering the lowest price for any given component.

To give you recommendations on which processor to choose, it would help to know an approximate budget. The processors you listed all sell for different prices. For your purposes, though, I don't think you would need the i7 processor. In fact I think you could probably get by with one of the slower i5 models (2300) or even an i3 model, assuming you aren't running any particularly demanding business applications.

Power Usage - Yes you should be concerned about power requirement of the CPU as you probably have a bare basic PSU (Power Supply Unit)
Your current G620 uses 65 Watts

Categories of chips: i3 processors typically have 2 physical cores. 2 or 4 for i5 processors, and up to 6 for the i7. More cores generally mean it can get more things done and faster. For work you shouldn't need more than an i5

The numbers after the Core type refer to the specific product model. A higher number means its better. Some are designated 't' or 's' they are lower power consuming versions. 'k' versions means it can be overclocked. You don't need to overclock.

You can get an i3-3220 for about $125