You should have goals in all parts of your life including climbing and mountaineering. Sure it is fun to climb leisurely and just do a peak here or there, but having a goal and a list to check off makes it even more fun.
The most common list to finish is the 14ers. There are between 52 and 59 total 14ers depending on how you classify them. Most people consider there to be 54 true 14ers in Colorado. You can find a list of them here. Some have climbed them all in a summer or in a lifetime. Whatever works for you.
Then there is the top 100 peaks in Colorado. The top 100 ranked peaks are basically all peaks over 13,800. Choosing to do the top 100 instead of just the 14ers gets you up on some awesome high 13ers.
A few people have climbed all of the 13ers. There are 584 ranked 13ers. Making a total of 637 peaks over 13,00o feet.
Then there are the county high points. These range from getting out of your car at an intersection in Denver to some gnarly peaks. But it is fun to climb the highest point in all 64 counties.
Then of course you can break it down county by county and try to climb the ranked peaks in each county.
Choose what works for you. Many start with the 14ers and work their way down as far as they can. The important thing is to have fun. So get out there and start checking them off.