This link will help, but info is hard to come by:
http://nagoyasuzuki.blogspot.com/
The link isn't direct and the site is hard to use so here is a cut from it:
Suzuki Violin Company - Nagoya
Suzuki Guitar, or Suzuki Violin Company Nagoya (hereafter referred to as Nagoya Suzuki), is from the Nagoya area of Japan. One reference says...
"Masakichi Suzuki was Japan's first violin producer. His father was a samurai moonlighter and made shamisens in Nagoya. Masakichi succeeded his father's craft business that soon failed. In the push for westernization in Meiji, he naturally became interested in shamisen's western counterpart: the violin. In the 1880s, he started to manually produce and sell violins. He founded the Suzuki Violin Factory in 1900. By 1910, his factory was producing 65,800 violins per year. Nagoya became the manufacturing center of string musical instruments...
Suzuki Violin Co., Ltd.1-1, Hirokawa-cho, Hakagawa-kuNagoya 454-0027, JapanPhone: 52-351-6451Fax: 52-351-6453"
Suzuki Nagoya seems to be somehow a cousin of, and is as well respected as, Kiso Suzuki. Their guitars says 'est. 1887' but that date has more to do with their production of violins. The production of guitars seems to have started, like Kiso, in the 1950's. One web source claims that there is no relationship between Kiso Suzuki and Nagoya Suzuki. But the model numbers are so similar there seems to be more to the story. Both companies made guitars that commonly have a laminated back or sides, many times the top also is laminated, but the sound, playability, and volume are what makes them so popular. Both Suzukis used a very high grade of laminate and the construction usually shows a high degree of craftmanship.
Suzuki Nagoya made violins and mandolins, and is still in business making violins, but no guitars. They seem to have stopped making them around 1989.
Suzuki Nagoya had a 'Three S' brand of guitar that seems to be consistently very highly valued by everyone that owns one. 
They also produced an "Insignia" series of guitars in the 80's that had solid woods used in the manufacture and had more of an electric guitar-type of neck - thinner than a typical acoustic guitar.
------------------
Now I own a M Suzuki Nagoya FW516 which is not a 3S brand and has M Suzuki inlaid on the head. Also it is not made by the traditional Nagoya company - Suzuki Violin Co., Ltd, but by Suzuki Instrument Mfg Co LTD instead.
So I can only presume that M Suzuki guitars are the Insignia guitars, not the 3S brand and are pretty special out of the Kiso Suzuki and Nagoya Suzuki bunch.
I bought mine in 1981 and have gigged with that for decades. So I bet that yours was made around the early 80's as Nagoya and Kiso stopped making guitars in 1986/7. The 3S brand ( 3 'S' letters intersecting at 0/60/120 degrees) was reasonably common in the mid to late 70's (I was there so I know 

 ), but the M Suzuki brand only surfaced for a few years.
The number in the model lineup is related to the cost of the guitar. So a W300 was retailed for 300,000 yen, a W516 was retailed for 500,000 yen. The F means 'folk' The W means 'western'. The FW516 has bound headstock, fingerboard, top, 3 piece rosewood back and a laminated spruce top (I think), compensated bone saddle and nut. Tuners are top quality.
Hope all this helps.