This is the list of the firearms that the 353 was issued at the very beginning. I have translated the original document into English and have presented the most likely weapon being described as well as the relative percentage of total.
January 1, 1944
Kriegsgliederung der 353.Infanterie-Division
(Stand: 01.01.1944)
I. Deutsche Waffen German Weapons
5.803 x Karabiner 5803 Kar98k rifles (60%)
171 x Zielfernrohrgewehre 171 Kar98k rifles with scopes (1.7%)
288 x Gewehre 41 288 Gewehr 41 semi automatic rifles (3%)
435 x Gewehrgranatgeräte 435 Kar98k rifles with grenade launchers (4.5%)
610 x Pistolen 610 P08 Luger and Walther P38 Pistols (6%)
2.372 x Maschinenpistolen 2372 Mp40 submachine guns (24%)
II. Beutewaffen Captured Weapons
27 x Gewehre (it.) 27 M91 Carcano rifles (0.3%)
Kopfstärke: 13.584
http://www.forum-der-wehrmacht.de/index.php/Thread/29564-353-Infanterie-Division/