Any Base weapons unlocked during a MWII Season, Event, or other unlock challenge (e.g., the Tonfa Base Melee weapon, available only as part of the Vondel Event in Season 04).
All Modern Warfare II weapons will be available for Modern Warfare III players, although each weapon’s associated unlock challenge must be completed before it becomes accessible in MWIII. Any Blueprints also carry forward, and certain MWII Blueprints available via Store Bundles will also be available to purchase in MWIII.
Some Base MWII weapons were available for a limited time during MWII’s Seasons of content, and are initially inaccessible to MWIII owners, unless the specific Weapon Unlock Challenge for that weapon has been completed.
To reiterate: If you haven’t played MWII and pick up MWIII, the full complement of MWII weapons will be available, but only after the associated weapon challenges in MWIII are completed.
Therefore, Modern Warfare III players should expect the following Base weaponry accessible in the Gunsmith, at launch:
COD MW3 Bot Lobby, Boosting, Accounts