Everyone's popping out their personal preferences, but let's see if I can give you a more comprehensive discussion of your options.
First, let's talk about what brand/style of plane you should get assuming you know what size you want.
Option 1: Pay a bunch of money for a very well made metal-body plane that is well-tuned and adjusted out of the box. Lie Nielsen and Lee Valley are good examples. Hone the blade, and they're ready to go. Excellent tool, tight tolerances, right out of the box. Lots of money.
Option 2: Pay a smaller amount of money for a cheaper new plane. Modern day Stanleys are an example. Cheap enough, but it will need tuning -- the sole will not be flat, may not be square to the side, etc. You can fix all of this. There are plenty of websites and books that will teach you how, and it's easy. It does take a bit of time and elbow grease, though. The blades and chipbreakers in these planes tend to be thin and flimsy. You'll want to replace them with a good blade and chipbreaker by Ron Hock. Expect more slop in the adjustments, which takes a little more patience when using.
Option 3: Buy an old used Stanley-Bailey off e-bay. This is very similar to option 2. But the old planes were better made than the new Stanleys, so when you are done you will probably have a better quality plane. You'll probably need a Hock blade and chipbreaker too.
Option 4: Woodies. Old-fashioned wooden handplanes are one of the most enjoyable tools in woodworking. Steve Knight makes them (by hand) today, and his planes are outstanding. They are also a lot less money than the high-quality new planes, and you'll pay about what you'd pay for a used Stanley - Bailey with a Hock blade and chipbreaker. (Steve Knight's planes come with great blades.) You can buy used woodies cheap, but they may need more adjustment than a new Knight. Woodies are super easy to keep tuned (wood sands flat and true much easier than metal). You can also buy Japanese-style wooden handplanes, which are also very good. Most woodworking stores carry them, as does JapanWoodworker.com. You have to get used to adjusting the blade on woodies --- you tap the blade with a hammer or the plane body with a mallet instead of the turn-screw style adjustment on metal planes. But once you get the hang of it, it's just as easy as adjusting blades on a metal body plane.
Option 5: Make your own. Yes, I said make your own. It is not that difficult. If you lack confidence, your local Woodcraft probably puts on a "making your own handplanes" weekend workshop you can attend, and almost any of the numerous hobbyist woodworking schools offer classes on making your own handlplanes. There are also plenty of books on making handplanes, and you should be able to check one out at your local library. You buy a blade (usually a Hock) and, depending on the style of plane, a chipbreaker, you take your own wood, and you make it into a plane. You get a very high quality tool when you are done for the price of a blade and a little wood.
Personally, I have some Lie-Nielsens, some Lee Valleys, some of the tuned-up e-bay planes, and some Knight woodies. I love them all and use them all. I pick up the woodies the most, as I really love the feel they give (and great results). But I have to admit, the Lie-Nielsen planes are probably the best-made tools I have ever seen, planes or otherwise. When one of my other planes is struggling with a particular cut of wood, the Lie-Nielsens always come to the rescue. They really are perfect. But you pay the price for it.
I haven't made my own planes yet; that's on the list of things to do soon.
In terms of what planes you "need," that's a trick question. Generally, you need a block plane because it does things other planes can't (because it's small). The rest all do the same thing --- they hold the blade in a fixed position relative to a flat sole. The difference is (1) the length of the sole, and (2) how you chose to shape the blade's edge and adjust the plane's mouth.
Smoothing planes are short planes, so they can ride up and down in any minor dips in the wood and give you a fully planed surface. You generally shape the blade to a small curve with the corners slightly rounded so you don't leave "edge marks" in the wood. You usually keep a very narrow mouth to minimize tearout.
Jointer planes are at the other extreme. They have a long sole, which ensures that the blade remains in a flat plane and does not go up and down with dips in the wood. This allows you to plane a surface flat. You usually have a perfectly flat edge on the blade because when you are edge-jointing, you want a perfectly flat edge and not a concave edge. You tend to have a somewhat wider mouth to accomodate thicker shavings.
Jack planes are just that --- a jack of all trades, master of none. It has a mid-length sole, so you can do a decent job flattening but still ride the peaks and valleys of the wood to get a fully-planed surface.
There are many other types of planes (and many in-between sizes), but these are probably the staples.
In terms of priority, a block plane is usually the most used tool in any woodworking shop, and it is in mine. So that's first. People like the low-angle block planes, but any good block plane will work just fine.
The next priority depends on what you do. If you want to thickness highly-figured guitar backs and sides, a smoothing plane is a good idea. If you want to joint backs and tops, a jack plane or a jointer plane is good. I strongly prefer the jointer because it makes perfect results very simple, but a lot of people do just fine with the jointer.
Although I respect everyone's recommendations, I don't think anyone can offer a meaningful suggestion unless we know your budget, what you building (just guitars, furniture, etc.), what tasks you want to use them for, and what kinds of woods you use (highly figured hardwoods plane very differently than straight-grained mahogany). Give us some more details and I'll be happy to be more specific with some recommendations.
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