Fleet Bonuses
Fleet Credits are the main currency used for buying fleet provisions. These are acquired by contributing to fleet projects, which you'll find under Fleet Holdings in the Social & Team menu. Usually fleets will have either provision projects in progress, or experience gaining projects for the various fleet holdings. You'll have the option to contribute different things, though usually the most common required are Fleet Marks. Fleet Marks can be acquired from PVE queue reward boxes that are usually an option. More information on that can be found on the Reputation page of the Walkthrough. Fleet Marks reward credits in a 1 mark:50 credits ratio. Energy Credits are at 100EC:1 Credit, so they're the worst to contribute. Don't contribute Dilithium, as that would be needed for buying items if you need them.
Fleets can combine together into Armadas, with one Alpha fleet having three Beta fleets, and each Beta fleet having three Gamma fleets. Within the Armada, The Alpha fleet gets the best Experience boost. This isn't entirely important as you'll get to 60 with one character doing all the story achievements, but if you're wanting to level up significantly faster, this can be helpful. Beta fleets are even with Experience and Dilithium bonus, while Gamma fleets are weighted to provide a Dilithium bonus. You can view the fleet holdings of other fleets in the Armada, and typically they're more welcoming to new players in their fleet if they come from another fleet in the Armada.
The Dilithium mine has a duty officer that gives rather decent development experience jobs, as well as an assignment that lets you refine an extra 500 dilithium a day very quickly. Preferably, the fleet should have this at level 3.
The Research Lab is one of the more useful buildings, so I would strongly advise finding a fleet that has it at level 3. When you beam into the interior, the very northwest of the lab has two mission NPC's. One gives you a duty officer daily mission that will grant you extra R&D experience upon completion, and the other has a regular quest that requires you to complete a specific R&D project in whatever field you choose. This requires quite a few crafting materials that you can aquire from queues or buy off the exchange using your Tour the Galaxy credits, but can give you an additional 5,000+ experience in your chosen school each day. The research lab, if it is ranked high enough, also allows you to buy another R&D slot, as well as extra traits. These cost quite a bit of fleet credits, but could be useful. You can also purchase green, blue, or purple Research Lab duty officers if you need more for crafting. Purple officers can help you crit on research projects, which will provide extra experience with each project.
The Spire contains many of the better endgame items, so ideally you would want this at Level 3 as well. You do need permissions from the fleet to buy items at the vendors, and most fleets have a 'contribution requirement', where you only get permissions after you've earned so many fleet credits with the fleet. Buying items from vendors are the only things that require permissions, everything else is available to every member. The Elite Fleet Efficient Combat Impulse Engines are a good choice to improve your Tour the Galaxy if you don't have the reputation for the Assimilated Borg Impulse Engines, as they increase your sector space speed.
The Starbase, on the far left room directly ahead of the Transporters, has a personnel requisition officer. For Fleet credits, you can easily pick up more duty officers that can help fill out your complement and allow more missions to be performed. There are more items in the north section of the starbase. Depending on the level of the starbase science labs, being in the fleet will also provide you with more transwarp destinations.