I've hike two 14'ers and a few 13'ers in Colorado. Here's a trip report for
Mt Sneffels.
Snow hangs on for quite a while in the highest peaks. You can expect some snow in June, likely into July if it's been a good snow year. Someone with local knowledge can let you know which places are likely to have more or less snow.
Starting elevations vary a lot, depending on whether or not you have a good 4x4 to get up to some of the highest trailheads. We started our hikes between 8 and 9 thousand feet but some trailheads are higher.
Trails down low are similar to trails here, far fewer bridges though and more cows. Once above treeline there is a lot more route finding than trail following depending on which peak you choose. In many places there are multiple routes and you must keep an eye out for where you are trying to go. The popular peaks have pretty well established trails and routes. We had clear weather and except for one unscheduled trip across a boulder field we stayed on track the whole time.
Your biggest concerns should be altitude and weather. Anytime you venture above 9K (depends on the individual) you can experience altitude sickness. Some people are much worse than others, there's no way of knowing until you get there. Spend some time acclimatizing, spend at least 2 nights at 7-8K before ascending too high. Drink lots of water, altitude is dehydrating. Know the signs of altitude sickness and keep an eye on each other. If in doubt, go down.
Most afternoons there are thunderstorms on the peaks. You should be summitting by 1:00 and get down. It is extremely dangerous to be caught up there in bad weather, and the storms come in most afternoons. Don't push on when clouds are gathering, keep an eye on the skies.
-dave-