I'm assuming that when you sat you have "3 high gears", you mean than you have a triple; Three chainrings. Triples, as you note, give you more gear options ( but not a third as many more, because you don't want to ride in the large/large small/small combination ). Generally, triples will have a smaller granny-gear than a Road double, which is handy when you're climbing hills.

As for figuring out what you need... well, what do you use the bike for? For example, I just swapped out my 50/39/30 cranks on my touring bike for a 44/32/22 set, because I'm old, fat, slow, and like it that way. :-) For commuting, unless you're climbing the Rockies to and from work, that's most likely too low. A fit recreational/racer would fall over laughing, too.

So the first thing is to explain is what you want to use the bike for.

Next, there may ( or may not ) be additional parts you'll need. Bottom brackets, for example, come in a variety of types and sizes. You'll need one that goes along with your crankset. In the case of systems like Shimano's HollowTech, the BB is effectively part of the crankset and will come with it. In my case, I went from a Shimano Octalink BB/crank to a HollowTech one, which also required a bit of simple machining ( which any good bike shop can do ) called "facing and chasing". Thankfully, all of this is cheap - my LBS charged me $32 for the machining and swapping out the cranks.