Normally you don't have to worry so very much about the difference between Japanese and Chinese readings so much because normally you're not trying to coin your own words.
Japanese was originally a completely independent language from Chinese, so in general words with a Japanese reading feel older than words that use Chinese readings. The further back in Japanese history you go, the less common Chinese readings are. (Of course Chinese readings exist in all of Japan's written history, simply because Japan didn't have a writing system until they borrowed the Chinese system. )
This is why Toritoribe-san a few post back suggests that the Japanese pronunciation sounds more feudal.
Shima and Jima are not pronounced the same. The difference between voiced and unvoiced is simply whether or not you vibrate your vocal cords. (For example, say very slowly the English word 'shoot'... you'll find your vocal cords are still until you start the vowel. This is the same 'sh' consonant sound in Japanese transliteration.)
I can't think of an actual English word using the right consonant sound for 'jima', but in any case it's the 'j' of the French name Jacques or the famous palace Taj Mahal. (The 'j' of 'jelly' is definitely wrong. The guide on wikipedia suggest 'j' of 'jeep' but I'm not sure about that. I guess it depends on your accent.) Anyway the sound is this one,
Voiced alveolo-palatal affricate - Wikipedia, the free encyclopedia
'hi' doesn't go directly to 'bi' just by voicing it.
'hi' is not voiced, not plosive (your lips start and stay open) 'pi' is plosive but not voiced (same consonant as 'hi' but you start with your lips closed and make a little pop as you start.)
'bi' is plosive and voiced.
(These are the same as most American pronunciations of 'h', 'b' and 'p'. There are some h's that I'm certain become a different consonant in some British accents, but American accents are too close to home for me to immediately identify any exceptions for these three consonant sounds. They probably exist, but in in case the h/b/p consonant sounds are all found in the broadcast standard American pronunciation of 'happy birthday'.)
Edit: Oh, wait. I forgot (again) that the h in 'hi' is not the h in the rest of the row. Japanese ears and English-speaking ears both group them as the same consonant so they're the same row in Japanese kana and the same letter in English but they're not actually the same sound. 'h' in 'hi' is the 'h' of a British 'hue', while ha/ho/he are the 'h' of 'happy'. Of course this is one of the subtlest points of Japanese pronunciation but, well, there it is in the extremely common word 'hito'.
This page is helpful starting point for the actual pronunciation of Japanese... you can always follow the IPA symbol link to get a recording of the sound (just keep in mind that an unimportant vowel sound is included in recordings of consonant sounds just to make the consonant pronounceable):
Help:IPA for Japanese - Wikipedia, the free encyclopedia
Actually pronouncing Japanese correctly is pretty difficult to do without actually studying the language enough to understand and mimic actual spoken Japanese but having the right consonant and vowel sounds is an indispensable starting point.