Here's an answer posted in http://goo.gl/Yb3nFj , pasted here in parts for your convenience. This 手 originally conveyed a nuance of "handling," "doing," "dealing with", etc. and only later started to take on a more general meaning. So, speaking generally, the plain adjective might have many meanings, including gross physical ones, but the 手- version tends to refer to behavior or at least some implied "use case." 堅い = hard, solid, rigid, tough, firm, stubborn (of objects and people, physical and metaphorical) vs 手堅い = sure, firm (of behavior/attitude) ぬるい = lukewarm, tepid, sluggish (of things and people, physical and metaphorical) vs てぬるい = lenient, non-harsh (of behavior/attitude) 狭い = narrow, restricted (of places/viewpoints/etc., physical and metaphorical) vs 手狭 = narrow (of places, when considered in the context of some [implied] behavior) 短い = short (physical, metaphorical) vs 手短か = brief, concise (of a text, etc.) Another example: in Nishiwaki Junzaburo's translation of Shakespeare's 18th sonnet, the "rough windes" that "shake the darling buds of Maie" are 手荒い: "手荒い風は五月の蕾をふるわし..." The winds are active, they have behavior. (There may be some anthropomorphizing going on here too.)

Part 2: As a related observation to the above, note that there are no 手 words for adjectives conveying purely emotional states (e.g. no 手楽しい or 手悲しい) or characteristics that are observed rather than "received" as behavior (e.g. no 手美しい or 手明るい). I don't claim that this is a hard-and-fast distinction, or even a completely reliable rule of thumb -- and as noted the prefix did slide towards a more general intensifying meaning -- but it might be helpful when considering how these adjectives differ from their unprefixed versions. Some other observations: 手- is not "productive" in Modern Japanese. That is, you can use 手- words that are already in the language, but you can't attach 手 to any adjective you like (not without thereby coining a new word, anyway). 手- does not combine with Sino-Japanese words or other loanwords. There is no 手丁寧な or 手ハードな. ************* As for the difference between 始め and 手始め, 始め is probably more general than 手始め which can only be used for physical-ish things like start of a vacation or start of class. In addition to that, 始め can also be used for emotional/metaphysical things like the start of loving someone or the start of a sunrise. Please correct me if I'm wrong.