Kac... Well congrats on making the big decision. First thing I would suggest is to search on bluewater boats here and read the already existing threads as a lot of what you ask has been discussed quite thoroughly. After that you may have more pointed questions to ask.
Here's a list of one guys take on what are "bluewater" boats worth considering which can give you some models to look at on Yachtworld.com so you can see what is appealing to you.
It is not comprehensive...and leaves out Tayana entirely (which I of course disagree with since the 37 is a classic world cruiser) but it is a starting point.
How big a boat are you considering and what is your maximum price range? Will you be single-handing or having crew? Are you looking for new, slightly used or very used? Here's a couple of very brief answers to some of your basic questions:
Masthead rig means the jib/jenny is rigged to the top of the mast vs. a fractional rig where it is rigged lower and has less sail area. Typically mainsails are bigger on fractional rigs and the mast is a bit more forward than on a masthead rig where the jib is both more powerful and harder to handle do to size.
Displacement is a measure of the weight of the water the boat displaces and tells you relatively little about the performance as a 20000 lb displacement can come from anywhere on the boat...from the masthead to the keel...but that is still how much weight the wind will have to move. Many blue-water sailors prefer heavily built high displacement boats but new materials and production techniques have some opting for lighter, more easily driven boats that are nonetheless seaworthy.
A cutter is a boat with two headsails..see my picture above of a cutter rigged ketch!
Keels go from full to cutaway forefoot to fin, to bulb to wing to centerboard. Full or cutaway forefoot keels tend to be found on heavy displacement traditional boats. They track straight and have little leeway and offer protection to the rudder and prop. They tend to be pigs for docking manoeverability and backing up. Fin keels are found on the majority of boats today as they are quicker and more manoeverable and still can provide lots of ballast to keep the boat stiff and upright. Sometimes the fins have wings on them to allow a more shallow draft and still keep the weight low but wing keels tend to get stuck harder around when you do find shallow water as we all do! Bulb keels put all the weight down deep but are generally more suceptible to damage and typically found on racer/cruisers.
Combined with these keels are either spade rudders which are fast and help manoueverability as they are a "blade on a post" but they are more prone to damage since they hang freely. Skeg hung rudders are less quick but are supported in multiple places by the hanging skeg part of the hull which also protects them.
Contruction of hulls in "fiberglass" is a huge subject since both quality of construction methods and advanced construction materials exist today. So...I will just say for now that the biggest differences people focus on are the use of "chopped spray on fiberglass" vs. hand laid up glass mat, and cored hulls (which are esstentially a sandwich of balsa or foam between two fiberglass skins). Cored hulls MAY be light, fast and strong AND may be used just above the waterline or on the entire hull. You can see the debates on this on other threads...but the big risk of cored is water intrusion between the layers and delamination as a result.
OK...go read and come back with more questions!