In reply to jafferton91:
This link may be helpful:
https://www.thebmc.co.uk/climb-skills-moving-together
Obviously any system you use will depend on the experience / skill level of each member of the team and the nature of the terrain. I cannot emphasise enough the need for all members of the team to have the appropriate knowledge, skills and practice. The consequences for getting it wrong could be dire!
Assuming easy ( for all members of the team ) rock or mixed ground and the person leading is the most experienced and the two people following have the appropriate skills I would suggest your second option. As the leader try to use natural anchors where possible ( threading the rope around stable spikes and blocks or either side of a ridge ) and using slings if required. If needed ( depending on the terrain ) then obviously placing cams ( I find having two or three mid range useful ) is also quick. Often you can find some fixed gear on popular routes ( check to see it is still solid ). Obviously wires or hexes can be used too, they tend to slow everything down so there is usually a compromise between speed and security. You will have to learn how to judge what is appropriate.
When you run out of gear re group and carry on. If there is a more tricky section consider setting up a suitable anchor, bring up the 'seconds' and the leader being belayed on that section and then the leader can belay the two seconds past the step before resuming moving together again. On technically more difficult sections ( for the party ) then moving together / simul climbing with micro traxions may be appropriate.
I would suggest your first method would most commonly be used when pitching as a three. It may be appropriate if there is a highly skilled / competent leader ( such as a guide or very experienced and capable alpine climber ) when moving together but the consequences of the second or third slipping don't bear thinking about.
Remember, practice, practice, practice. UK scrambling ground can be ideal to develop those skills on. If in doubt, try to find some experienced alpine climbers to learn from or book a professional.