standard federation recruiting channels. you will get all you need this way1. How would you actually go about recruiting soldiers, (must be volunteer only)?
a full body semi powered environmental suit would be the way to go. tricorder built into one of the forearms large enough to be manipulated with a gloved hand. air filtration units and 1-5 hours of air depending on the mission. standard issue rifle with phaser pistol side arm,2. How you you equip them, (can only use technology demonstrated in the various media, no 1-off superweapon stuff).
and a combat knife as well. assorted other equipment per mission requirements.
primarily an assault ship design used for full scale battles where military might is required. other then that redesigned shuttle craft capable of holding 14 to 20 people or serving as CAS (close air support).3. What vessels would you have retrofitted or build additional, (again, keeping within established and fully realized technology)?
primarily deployed with vessels with assault ships would be held in reserve. Units would be broken into 6 man squads(standard transporter sizes are 6 person) 4 squads per platoon, 5 platoons to a company, 4 companies to a battalion. each section from platoon up will include a command staff. the units would be deployed on ships based on size- galaxy class would likely house 1 to 2 companies depending on mission parameters. smaller vessels would normally hold 1-2 platoons. assault ships would hold battalions.4. Where would you station said soldiers, (keep a contingent on board all vessels, keep them in reserve to deployed only when needed, etc)?
training would be centrally at one location. and all training will take place there. saves a mountain of logistics. training will be about a year long including specialized training for combat medics and engineers, as both seem to be regularly needed in normal operations. Training would also need to include CQB and ship boarding and repelling training as those are also common. also include EVA training. The troops will be trained to operate in independent squads to be able to fully utilize the advantages that transporters allow you but also have combat shuttles available as well.5. How or where would you train said soldiers?
The chain of command would be separate for fleet personnel and soldiers. with the exception that the ranking solder would report to the ship captain.6. How would the chain of command function, (reports to ship's captain, has separate directives, give them their own vessels to operate)?
7. Any other significant points you'd address or policies you'd enact? Would you further break this force down into more specialized squads/corps, perhaps?
The main thing to remember is that the star trek universe is not a very militarized one as a whole so fielding large standing armies would be a wast of time in most cases since they wouldn't have a whole lot to fight against.
My strategy here isn't to create a wartime fleet and army but utilize the resources available to establish better security and safety of key crew members in potentially hostile scenarios. In the series' most conflict is resolved relatively peacefully or where small man teams are able to eliminate hostilities. using this experiencing in mind having 6 man operating teams, 6 being the most standardized number of transporter pads per room. create an effective fighting force that can combat almost any situation seen in the ST series. At a fraction of the cost of fielding entire armies.