The Japanese equities market has two major indices: Nikkei225 and TOPIX. Nikkei225 is the 'older' index and not capital weighted. Like the F.A.Z. index in Germany it was published first by the main Japanese business newpaper the Nikkei shinbun. The index is based on fixed allocations and is restricted to 225 companies. Compared to that the TOPIX has much more stocks (more than 1.300) composing the index with a capital weight approach. Even so the capital weight approach is becoming more popular around the world the TOPIX has two drawbacks. First - there are to many companies in this index. In Japan many very small companies are listed and second - the trading hours for TOPIX futures are less liquid then for Nikkei after the stock exchange closes at 3pm Tokyo time. This makes it difficult to hedge positions taking into account the direction of the European opening markets.
Recently ETF's on the Nikkei225 and TOPIX became quite popular. Those are a low cost and efficient way to participate in the Japanese equity market. My recommendation is to focus on the Nikkei225 - other Nikkei indices never became popular.
Gradually I will give background information on the companies listed in the Nikkei225 including the traffic ligth rating. More or less all of the companies listed in the Nikke 225 can be traded in Europe. An easy overview can be found on the ingdiba webpage you can find below.
Links: www.tse.or.jp/english (Tokyo Stock Echange - TOPIX)
http://www.ose.or.jp/e/ (Osaka Stock Exchange - Nikkei index225)
(Nikkei Index published by Nikkei Shimbun - Japanese Economic Newspaper)
Webpage is in German, but should be understandable how to use with basic German language knowledge