If you think in any language you're never misstaken on what word you mean even if there are many words that are spelled/pronounced the same. This causes a language with only one word meaning every possible word there is to work, in theory, if used only while thinking. I don't think I'd be able to think clearly in such a language, though. The fastest language seems, for me, to be no language. It is however hard to not think in a language.
What is the fastest language to think in?
With your question you are limiting thinking to conscious and rational thought. But human information processing has so many more aspects, some of them faster and more efficient than cogitation.
If, for example, you sit in front of the computer and have forgotten that you have put water on the stove, and suddenly you hear the noodles cooking over, you'll jump up and run to the kitchen quicker than you can form the sentences that describe what is happening and what you need to do. It is not a reflex (like flinching away from being hit), but clearly a conscious understanding, a consideration, and a decision, only not verbal. For me, parts of that process are visual (I see what I need to clean away, when I hear the water hit the hot plate), others include a body-memory projection of me moving to the kitchen, a muscular plan of action that is forming while I jump up, see what is on my path, and "pre-feel" how I will navigate it at maximum speed.
Another example is what I have often experienced when I "sleep over" a decision; what has been exemplified in Einstein dreaming of relativity theory; and what I have read about again a few days ago in a book summarizing current research on intuition: that conscious rational thought is only able to make decisions in situations with a limited complexity (the level of complexity was the focus of some research), and that highly complex decisions, involving too many aspects to "juggle" in your (conscious) mind, are made on an unconscious level, with "you" (that is consciousness) only receiving the outcome (that is intuition) of that information processing.
Language is a very recent development in evolution, and consciousness is not much older, and it is my opinion that we are misled by our self-identification with the constant chatter in our minds to believe that we are this speech, while in truth language and consciousness are just tools that are as peripheral to our core selves as our arms are to our bodies. There is this famous experiment, conducted a few years ago, that showed that the muscular impulse for a movement happens before the conscious decision for that movement is made. It shows that what we perceive as decisions happens after a behaviour has already begun. The ego, as Freud said, is not master in its own house.
I wonder if Hungarian is particularly good in this way. It's agglutinative, like German, so the words can be unbearably long, but the grammar of Hungarian is interesting, in that word order is much more flexible than other languages. Sentences can be said in multiple word orders and still be "correct", while the emphasis required by word order gives nuance and helps to shape the precise meaning of the sentence. The Wikipedia entry gives some examples. I'd think that having that kind of flexibility available in a native language would be a benefit... I've heard that the grand history of science and mathematics in Hungary is credited to the kind of mental flexibility that speaking Hungarian offers. In some sense, math's commutative and transitive properties are built-in to the language itself.
Full disclosure: my knowledge of Hungarian consists of a few common words and phrases, and lots of food words... I do love the food in Budapest.
There are also many constructed languages that are specifically designed to facilitate thinking, but, of course, they're not in wide use. Ithkuil and Loglan are well-known examples.
I remember some empirical research showing that “wordy” languages were spoken faster than more information-dense languages, so that the “information rate” would be more or less constant across languages (sorry, no reference). Of course, this research was concerned with speech rather than silent thought but it could suggest that you would not expect any overall difference between cultures in this respect, which does make sense to me. Note that studying this sort of things requires a lot of care and preliminary ground work as common notions like “word” are not even meaningful units in many languages. Linguists therefore use precisely defined concepts like “phoneme” to measure this.
Also, I would dispute that thinking “in” a language (see my answer to Is it possible to think in a second language? for a discussion of this idea) means that one is never mistaken on how to express oneself. The “tip-of-tongue” experience would suggest otherwise. Some thinkers even object to the notion that speaking can generally be seen as merely expressing some previously formed thought.
Sign language I would imagine would be a great language to think with since it is physical and involves body language. Considering too that we all think different I know sign language, Spanish, and English and find my thoughts bouncing from language to language. Also what could be considered fast? How do you rate the speed of thoughts and inner conversations in your mind?
