Weight, if you will only use the tent in the valley next to the car then weight doesn't matter to much. But if you intend to use the tent for backpacking you will have to carry it. Generally, you will be going into the mountains with others and sharing a tent. Therefore you will want to share the weight between the people using the tent. So ideally choose a tent that can be broken down into 2 or 3 similarly weighted pieces.
Materials, cotton is heavy but durable and will need to be re-water proofed every couple of years if used a lot. Also, it may shrink a bit over time, this material is good for people who work with kids as it can take the abuse. Nylon is light weight but will have condensation problems if you don't have adequate ventilation. Nylon may need re-waterproofing occasionally and is a bigger fire risk than cotton. Gore-tex tents are single skinned and hence lighter, but will be more expensive than the other materials.
Features, ground sheets this is the floor of the tent, these days most small tents have them sown in which means that the rain won't get in at the edges of the tent. Those that don't have ground sheets tend to be the large family frame tents that generally come with "bed rooms" and you can buy separate ground sheets to put on the floor. The thickness of the ground sheet does affect the weight of the tent and back packing tents tend to have thin ground sheets to save weight but they are easily punctured. So to prolong the life of the ground sheet itís a good idea to use a heavy duty separate ground sheet under the tents ground sheet when camping out "of the car" because you don't have to worry about the weight of it.