I sometimes confuse these; so, I am setting things straight.
The Latin abbreviations "i.e." and "e.g." come up very frequently in writing and would probably come up more often if people were more sure of when it is right to use "i.e." and when "e.g." is required. To me, the only way to figure it out is to know what they stand for.
"I.e." stands simply for "that is," which written out fully in Latin is 'id est'. "I.e." is used in place of "in other words," or "it/that is." It specifies or makes more clear.
I'm going to the place where I work best, i.e., the coffee shop. [There is only one place that I am claiming is best for my work. By using "i.e.", I am telling you I am about to specify it.]
"E.g." means "for example" and comes from the Latin expression exempli gratia, "for the sake of an example," with the noun exemplum in the genitive to go with gratia in the ablative.
"E.g." is used in expressions similar to "including," when you are not intending to list everything that is being discussed.
At the places where I work best, e.g., Starbuck's, I have none of the distractions I have at home. [There are lots of coffee shops I like, but Starbuck's is the only international one, so it's the only "example" that would work.]
I.e. and e.g. are such common Latin abbreviations that they do not require italicization.
If the form "I.e." looks odd, it's because both "i.e." and "e.g" are usually mid-sentence, surrounded by commas, so they are unlikely to be seen with word initial capitals.