Well, for your shooting, a few stats I might go with are:
Velocity - The Fps the round travels, Slower rounds with have more Damage, Faster rounds will provide you with Armor Penetration.
Damage - Different Guns will have different damage ranges.
Range - Range effects damage as well, the farther away you are, the less damage is dealt.
Accuracy - This is a separate stat for both the player and the gun. Seeing as both play a major role in hitting the target.
Firing Rate - How often the weapon fires. The faster the gun, the less accurate it becomes.

Those are some basic stats that can be used for the guns. As for quests, It's hard to say, but I'll try to give a few quest genre choices:
Kill x Enemies - These quests are grinding and require you to kill a certain number of a certain type of enemy. Or you can turn this into killing just one big enemy, like a boss.
Delivery - These quests require you to travel to some place to deliver or pickup various items, this often leads to longer quest lines that help develop the story better.
Dungeon - You go into a dungeon or an area that you must clear of a certain mob or something of that sort. Close to a Kill x Enemies quest but can often require more than 1 player and utilizes cooperation to survive on conquer.

For locations, there are literally endless possibilities for a space adventure game:
Capital Ship - The main Flagship of your faction, probably where your character will start out at. This is probably like a city in space, providing everything that your character will need, such as weapons, provisions, ammunition, upgrades, trainers, ect. It also might have a place for players not doing anything to trade weapons or just hang out.
Planet Surface - An area of a planet that the players can explore and quest on. You might want to have different planets for different terrain features, such as a Forest planet, where everything plant-like is massive, however jungle monsters are also bigger. Desert planet, long vast stretches of sand, players might explore ancient ruins as dungeons. Creatures here might be more reptilian, more suited for the environment. Also, Water planet, full of underwater reefs and whatnot, also the ocean being full of the most vicious of all monster, and since most of them look strange, you can let your iconner have a ball with creating these creatures. There are literally endless possibilities with this.
Abandoned Space Station - An old station that is now inhabited by pirates and other space lifeforms. This is a perfect place to host some of the darker dungeons.

That's about all I have for now, If you want idea's on weapons, just take idea's from games like Halo, Gears of War, and other great space games. Anyways, i hope this helps some, if you have any questions, just post them and I'll do my best to answer them.

Also what about horror monsters?