Different categories of bikes are not "better", just better suited for a type of use.

If I had a friend who drove a sports car and did Pilates I'd push them towards a road bike. For a friend who likes hiking and bull riding I'd push a mountain bike.
If you don't have a very clear idea of what they are likely to enjoy and focus on then they will probably be best served by an all-arounder. Something versatile, and, unless they're rich, affordable.

I would consider touring bikes and cross bikes the most versatile, but they also tend to be expensive (by my standard).
Older mountain bikes are also extremely versatile, and with a little luck can be had very cheap.

A friend of mine just started cycling Based largely on my recommendation he bought an older Trek 720 (hybrid), but if we hadn't found a great price on that bike I was going to set up an old Diamond Back Topenga for him.

Older mountain bikes will have 26" (559mm) wheels instead of 700c(622mm), but road slicks are still readily available so I don't see that as a serious down side, and it can be a major advantage. Lots of good older mountain bikes will be non-suspension, triple butted chrome-moly steal frame, 48t large chainring, and have rack, fender, and multiple bottle mount braze-ons, and can be found on Craigslist for around $100 or less. This really is about as versatile as it gets. I like drop bars, but because of the price difference and the perception of many non-cyclists I rarely push the matter with new cyclists.

It's also possible to covert a rigid mountain bike to 700c on the cheap. Check Gav Tatu's Flickr and you'll see some simple but brilliant V-brake adaptors. And many people have done drop bar mountain bike conversions (mostly with brifters, so not so cheap, but still cheaper than a new cross bike if you can do the work).