Both are correct, but the common approach is to use (2)
Effectively, 1 and 2 are the same sentence, but with words ommitted in (1):
- Hi, I'm Rei Ayanami, [a] web developer, based in Tokyo-3
Of note, is that this turns the sentence into a list of facts about yourself. As such, it tends to be used only when there's a specific/standard set of information you need to convey.
Hi, I'm Name, JobTitle, based in CompanyBranch, currently looking into ProjectRequirement
This would be where each person in turn is expected to give the same kind of canned response - filling in the blanks with their information.
An example of this in action, is the British TV show "University Challenge". Where the introductions follow a standard progression of:
Hi, I'm Name, from Place, studying Subject
The second sentence is much more complete, and would be expected when introducing yourself one-on-one or in a more regular setting.
The progression in this phrase is more flexible and gives more scope to provide details you think are relevant to yourself - without conforming to a specific format.
Hi, I'm Name, a web developer currently working for Company which is based in Place - and [here's some other information that's good to know about me.]
In general, the second form will be preferred as it gives a less rigid and therefore - more sincere - sounding introduction. This is also how most introductions take place, with the first version being only in specific situations.
Also of note, while the second form could come across too cold - the first form will likely never be seen as incorrect or too much. Even in a situation where the majority are favouring a list of details - you would not risk being rude to use the first variant.