Starships rarely beam down their entire command staff as a landing party. There are enough technical specialists on board a vessel to provide numerous landing parties for almost any situation.
Starships will generally have several action teams ready for duty. These may be permanent assignments or temporary. For example, a survey ship would have several permanent science teams while a warship might assign personnel as the need arises.
Action Team Organization:
A specific team's organization depends on the mission. A science team would have a science officer in charge of the team and a science specialist (this might be even further specialized into geology teams, botany teams, and so on). A medical team would have a doctor as the officer in charge and a medical technician.
The two Marines are assigned for team security, but may also be put to work on other duties (piloting shuttlecraft, operating equipment, carrying heavy items). The Marines may be replaced by additional specialists if required by the mission. If there are a large number of teams operating in an area, a Marine squad may be assigned as security to cover several teams.
This is a typical Marine squad found on just about any Star Fleet vessel.
Marine Squad Organization:
The heavy weapons specialist carries a light rocket launcher and a Phaser-2 pistol instead of a phaser rifle (each squad member carries a spare rocket). For boarding actions, the heavy weapons specialist leaves the rocket launcher behind and carries a phaser rifle.
These units are generally only found on commando vessels or ships with large Marine detachments.
Heavy Weapons Team Organization
The team is assigned a medium rocket launcher. The launcher is split into three parts (barrel, mounting, and computer module) with three members of the team each carrying one part and the other two members carrying spare rockets.
These are rare units that specialize in hit-and-run raids and unconventional warfare.
Commando Team Organization:
The team generally doesn't carry any heavy weapons, instead rellying on stealth and surprise to conduct their mission.
Most Marine detachment commanders on a starship will organize at least one boarding party into a strike team. This team will be the detachment commander's "go to" team and personal troubleshooters.
Strike Team Organization:
The Star Fleet technical specialist is typically from the Engineering Department and is well-trained in a wide variety of technical skills as well as having above average combat training. This gives the team better flexibility and utility in special situations.