So basically what you're saying, is that you're still at the tutorial (near the end of it anyways)
Every 10 levels (Level 10, 20, 30 and 40) you get a new starship of your own choosing. If you've chosen the career of Tactical, doesn't necessarily mean you need to stick with Escorts (which are better suited for damage dealing). Same goes for Engineer vs Cruisers, or Science vs Science ships.
There's quite a few additional ships that can only be purchased in the C-Store for "Zen" which is Cryptic's own currency. In order to obtain Zen, you can either purchase it from their homepage (for real cash), or participate in activities that reward Dilithium. In your "bag", you have an Assets tab at the top. From there, you can see your total amount of currencies (including Dilithium Ore / Refined Dilithium), as well as access the Dilithium Exchange.
The game can be played from 1 to 50, without spending a single dime. Inevitably, you'll end up looting a "lockbox" item. To unlock it, you need to either buy a Master Key from C-Store, or off of the Exchange (aka Auction House) for Energy Credits. Note however, that these keys are usually pretty pricey on the Exchange. Sometimes exceeding the maximum Energy Credits for a Silver Player (10 million). If you buy anything off of the C-Store, I highly recommend buying the Credit cap increase.
There's also an Account Bank, which is useful if you have multiple characters, for easy transferral of any non-bound items. This bank however is deactivated for Silver players, while Gold players get a 10-slot limit.
Personally, I'd recommend getting a 1-month subscription for the first month, as it also gives you free additional Inventory and Bank space on every rank up (including respec tokens at rank up). Even if you deactivate your subscription, you get to keep the inventory slots you've unlocked by previously subscribing.
Hope this helps a little bit. Feel free to ask more