Personally, as a player, I don't really like the "forced" conditions when I play a game.
I don't like limitations, I love freedom, I play for fun not for frustrations.
*
"Your mission Commander:Assault a Snakeman Battleship, you have to win and to kill at least 10 Chryssalids.
Equipments:1 Stun Rod, 1 Smoke Grenade, 2 XCom Grenades, 1 Armor (but, no Flying Suit authorized), 1 Medi-Kit, 1 Psi-Amp, 1 Pistol with 2 clips, 1 Rifle with 2 clips, no HWPs authorized, only 3 Rookies (total 4 units).
And you have to do this in 10 turns!
Good luck Commander, and use your equipments wisely!"*
Not my cup of tea.
Just imagine. Despite all the constraints, the player has successfully killed all the other units. He killed 9 Chryssalids, it's the tenth turn. He has only one ammo in the rifle that holds its last soldier. He may still succeed. The last Chryssalid (with only 1 life point left) is located at 3 tiles of distance. The soldier is kneeling, 92% chance to hit (and thus win the game). The player is confident. The soldier shoots and... ...miss...
Furious ... the player rises noisily and destroys his computer.
That said, your idea of special missions is great! I like it!
But as it's a tactics phase of the game, it's better to let the player to have the choice how to do it.
*
Mission:"Our Intelligence service has reported the delivery of a large shipment of a new type of Alien weapons.
We absolutly need these prototypes to know exactly what the Aliens prepare.
We know that the delivery will take place in the following week (from June 12 to 19) somewhere in Asia, but we don't know exactly where.
We have 5 hours to attack the UFO after landing.
Monitor your radars, and try to not shoot the UFO in flight, wait until landing.
Exceptionally, crew will consist of Mutons and Ethereals with Sectopods.
The report precise they are heavily armed, expect lot of Blaster Launchers."
*
Mission Bonus-Malus:UFO ignored: -2000 points.
UFO destroyed: 100 points.
Landed UFO assaulted: 300 points.
Weapons recovered: 100 points, 100 weapons --> sell them, use them.
New Alien Technology to research.
UFO crashed and assaulted: 150 points.
Weapons recovered: 100 points, 100 weapons (random, 10% chance to recover weapons, random weapon number).
New Alien Technology to research (only if at least 1 weapon recovered).
*
This way the player have full choice on what he want to do.