What is the best type of beer to brew for a beginner?
I always recommend an Ale of some kind.
For a beginner beer I always want to advise something that is a little simpler so that the beginner will have a better chance of success. I want them to keep brewing!
So, I would stay away from lagers, as they often require more equipment to keep cool. I also would stay away from sour beers as they can be more finicky.
I'll often recommend something with some character to it: either a little hoppy, like a pale ale, ipa, or american amber, or something roasty like a stout, etc. That way there's some grain/hop flavor to mask potential beginning mistakes.
But the best advice, I think, is to pick a beer the beginner likes to drink. There's no point making a beer you don't want to drink.
I agree with sgwill, but I would add that you also want to pick a style that can be done with just extract + hops + yeast. Not having additional grains to steep cuts time and effort off of that first brew day. One of the best I've used is a simple hefeweizen: 6-8 lbs. wheat LME + 1oz. tettnanger (60 mins) + Wyeast 3068 (Weihenstephan Weizen). Easy to brew, very tasty, conditions quickly.
I don't think the exact kind of beer matters, but I think you would be best with something like this:
1) Simple beers that only have a bittering component will take less effort than more complicated pale ales that have bittering, flavoring and aroma hops.
2) Something that is not high gravity. You want to start with something that is OG 1.070 or less, it just makes the whole progress easier.
3) Use dry yeast. You have a a whole bunch more yeast cells with the dry yeast. You don't need to make a starter and its cheaper.
4) Do a malt extract beer with some grains, but do not start with a mini-mash or all-grain.
Above all, you do need to brew something that you like, otherwise you won't want to progress and relax, have a home brew!