Probably the most important consideration, when choosing what type of guitar to learn on, is what type of music will be played on the instrument. If you're a fan of rock music, and want to learn to play rock guitar, starting on electric guitar is a logical choice. If, however, you're a fan of acoustic music, and want to learn to strum your favorite songs, an acoustic guitar is probably best for you. The importance of the above philosophy can't be stressed enough. If you get stuck with the wrong type of guitar, you're going to have much less motivation to pick it up and play it regularly. 
Note to parents: this same principle applies when picking out a guitar for your child. Try to realistically assess what they'dlike best, as opposed to what you'dlike them to play. Their progress will be noticably better when playing a guitar they like.
Ease of Learning

Depending on your personality type, this might either play a major factor in deciding which guitar to start on, or might be irrelevant. Some people find if they don't see results quickly, they get discouraged, and lose interest in playing guitar altogether. If you think you (or the person you're buying for) are one of those people, an electric guitar is probably the instrument to start on. Electric guitars have smaller bodies, smaller necks, and it's much easier to press down the strings. Essentially, you can start playing the *basics* of guitar much more quickly and easily on an electric guitar, than you can on an acoustic. Having said that, there are a few knobs and buttons on an electric guitar that can complicate using it somewhat. 
Budget Considerations

Understandably, paying a whole lot for a first guitar isn't very desirable, especially if you're not even sure if playing guitar is something you (or whomever you're buying for) will stick with. For this reason, acoustic guitars are more often the choice for a first instrument, since they tend to be slightly less expensive. Electric guitars require the purchase of an amplifier, and a guitar cable, so they can end up costing a little more. If you want to learn on an electric guitar, but budget is a serious issue, many guitar stores offer starter electric guitar/amp packages at very reasonable prices.

Making the Decision

Now I've given you some things to consider, it's time for you to decide which type of guitar is best suited for you, or for whomever you're buying for. Let's summarize - if the person in question frustrates easily, or listens to and wants to play "hard rock" music, definitely think electric guitar. If, however, the person in question wants to learn songs to sing along to, and can handle a slightly steeper learning curve, then an acoustic guitar might be in order. 
Once you've made a decision, take a look at the following page for a few recommendations on specific guitars to buy.