Welcome to the group, Mike
This suggestion has been made before but I can't find the thread.
Firstly, as people have already said, try
First Missions. This was what got me and many others on this forum into the game.
If you like
First Missions - and I'm sure you will! - then there are several options. You can do what you have already mentioned, and buy a Border module. This gives you the latest rulebook, maps, counters and ship cards. If you like
First Missions enough, then this is the way to go.
Thirdly, if you're still not sure after
First Missions, then you could do worse than buy the FC Reference Rulebook electronic copy from e23, or the paper copy direct from ADB. I think it's about $15 or so, either way.
This could be a cheaper way into the game for you because it sounds as if you already have maps and counters from SFB, which you can use with FC; all the tables you need are in the rulebook, and/or can be downloaded from the Commanders' Circle on the FC website, and you can flesh out your fleets by using the ship cards from the Communique newsletter.
However, to my mind, part of the magic of FC is the high-quality game components and the sheer richness of the game system. You will probably want to buy the real thing, I'm sure, but the ideas above will give you a cheaper entry path if you need it.
The advantage of buying the electronic rulebook, btw, is that you can download later editions for free (to a point; the price includes minor updates but not major revisions), incorporating all the latest rules modifications. Granted, you will get the latest rulebook if you buy a Border module, but the electronic copy may be something you might want anyway in addition to the paper one from your Border module, because of this flexibility.
I hope this is helpful. Once again, welcome aboard!
