Well, as an absolute first step, you can always give
First Missions a try. It is a free PDF download that gives the feel for the game and two ships to try with (Fed CA and Klingon D7).
Using just that, you can go through various published
Communique Newletters and pick out Federation, Klingon, Kzinti, Tholian, Orion, and WYN ships to try out those rules.
Note that in both cases, there are no maps or counters (obviously, as First Missions is just a PDF download),
After that, the easiest entry point depends on whether you have counters and maps or not. If you do have counters and maps, then the easiest way to start is just to buy the
Reference Rulebook and make use of the Communiques given above. This gives access to a huge portion of the game for just $15 (plus shipping). You can also buy a PDF version of the rules from places like DriveThruRPG and SJG Warehouse 23.
If you need the counters and maps, then the next step is
Federation Commander: Academy. This includes a paper map, counters, the full "Border" rulebook, and laminated ship cards for four ships. Do note that you can still use the ships from Communique to expand out your fleet. If you are happy with what you find, you can then get Federation Commander: Graduation, which gives the equivalent of Klingon Border (see below).
The main full entry products are the two Border products:
Klingon Border and
Romulan Border. These contain hard map panels, counters, sixteen laminated ship cards, and the full "Border" rulebook.
Do note that the Border Rulebook doesn't include everything in the Reference Rulebook. The Border Rulebook instead includes only the rules required for the two Border products, but does include the ship descriptions and some scenarios. The Reference Rulebook includes all of the rules, but no ship descriptions or scenarios.
I hope that helps!