I used to travel alone for business all the time. I actually prefer travelling alone to being with a group because the logistics are easier. (Just figure things out for myself and not worry about others' preferences or dilly-dallying which drives me NUTS)

As others have said, check in online the day before and print your boarding passes at home. It's entirely a preference thing whether you should check a bag or do only carry-on. I don't like hauling weight around, especially if I have to traverse an airport for a connection, so I always checked one bag and had one small carryon. Generally it's not a problem to connect in airports, there are usually well-placed signs telling you where the terminals/gates are.

As soon as you get off your first flight, identify the number for your next flight and look it up on the departure monitors. (If it's printed on your boarding pass, don't assume it's correct. Changes happen.) Then I go directly and immediately to that gate. If I get there and find I have time before boarding, then I'll go find something to eat. I also do this in the first airport: go immediately through security and find my gate before I do anything else, just in case there are TSA delays.

Always, always leave yourself plenty of time for screwups, and you'll have a no-stress travel experience.