Unsolicited advice.

So, you want to get your first classic motorcycle but you're not entirely sure what to go for. Maybe you already have, or have had, a relatively modern bike, or maybe you have a run of the mill car and family needs come first, but now you can finally treat yourself to that one special thing you've always wanted to see when you open your garage doors: a cool, vintage, classic motorcycle. Good for you man.
I've said it before, there is nothing cooler than a classic (British) motorcycle.

Well, understandably, one can feel a little bit overwhelmed by all the different makes and types of classics, where they come from and when they were built. They each have their own idiosyncrasies that you'll have to learn to live with, so what you're willing to put up with may well determine what you end up going for. (kickstart only, leaky engines, thirsty engines, vibration, high-maintenance...)

I think the very first thing to do is ask yourself one simple question: what would you like your motorcycle to do for you? Is it something you want to use once in a blue moon, for a quick blast on a sunny day, or is it going to be your back-up workhorse in all possible weathers? Once you figure that out, alas, it is a question of how much of your hard-earned cash you can/want to spend on it. Assuming we're not talking Vincent or Brough, you'll probably be looking at around six or seven thousand euros (or your local equivalent) tops. And the good news is that there is a lot to choose for that sort of money. I'll leave it up to you and perhaps a further discussion, whether to go for a running machine or something that requires restoration. Obviously a working motorcycle is worth more than some boxes of parts. Do keep that in mind.

If you're thinking of something to be used on those rare days when the weather is just right AND you don't have any other commitments, then you could go for something a bit extreme, like a single seater (be it a clip-on speedster or a rigid framed "chopper"), whereas if you want to be able to go anywhere, anytime, then you'll probably be looking at something with a comfier seat, upright riding position and rugged components throughout, from engine to lightbulbs.

Now, what type of engine would you like to have? Two strokes? Four strokes? Diesel? Rotary? Personally, I like four-strokers, but do try to ride other types as they are fundamentally different experiences.

I once heard it said that a motorcycle's character is inversely proportionate to the number of its engine's cylinders. That's a fancy way of saying that big, 500cc. thumpers (i.e. single cylinder engines) are great, as opposed to in-line fours that may seem to dilute the experience of sheer low-end torque.
Three-cylinder engines are somewhat peculiar, and you're really looking at the Triumph/BSA lump of the 70s, as well as Laverda.

Now, twins is where classics really shine and offer the most choice: you find them in just about every configuration you can possibly imagine, from the straightforward in-line, 360° British type, to the seemingly counterintuitive (Douglas' boxer engine anyone?). 'V' twins alone easily go from Harley-Davidson's iconic 45° angle to Ducati's brutal 90°(an 'L' twin, effectively). Each configuration carries with it different characteristics and you don't need to be an engine-sommelier to tell the difference. So again, try as many as you can before you pull the trigger. One thing they all have in common is that they deliver one of the most visceral experiences a motorcycle can: low-end torque. To me at least, that speaks louder than any amount of horsepower, electronic wizardry and top-speed figures. And though (on paper) a twin may not be as fast as a four, we're talking top speed here, they're by no means slow. Chances are, regardless of make and type of bike, a twin will make a perfect classic bike for you.

Now, can I assume that we're talking about something at least post-war? Not that there's anything impractical about a 1937 Velocette MAC, for example, but in this imaginary conversation I'm picturing the more likely scenario of a first-time classic buyer, and it is understandably more likely that someone would go for something built in the 70s or 80s. Again for practicality, I won't consider anything with an iron head here, so for the Brits we're generally looking at the early 50s onwards, while some others *cough*Harley-Davidson*cough* took a little longer to switch over to light alloy heads (though when they did, they did it really well and made the whole thing out of the stuff) and others still *cough*Laverda*cough* are rumored to never have.

Let's have a quick go around the globe to see who, in no particular order, has motorcycles worth having a look at:

Italy (Moto Guzzi, any of the 850 "round fin" in a Tonti frame; Moto Morini, any 3½ or 500, but have them well sorted by a specialist; Ducati, scramblers are cool as are any of the large capacity 2 valve air cooled twins; Laverda, no direct experience but both twins and threes have undeniable appeal.)

Germany (BMW, any 2 valve, air cooled twin from the late 80s.)

UK (Norton, Commandos of course, but also Dominators and the ES2 singles; Triumph, unit 500s either Tigers or Daytonas; Royal Enfield, any Bullet, 350 or 500; BSA, pre-unit 500 and 650 twins, or any 650 OIF; Ariel, no direct experience, yet, but I'd say any 350 or 500 single; AJS/Matchless, any "heavyweight" 350 or 500 pushrod single with an alloy head; Velocette, no direct experience, but they're mouthwateringly good looking and make wonderful scramblers as well as roadsters.)

Japan (the big 4 of course: Honda, Yamaha, Suzuki and Kawasaki. In-line fours is their specialty but don't forget some absolute classics such as Honda's CX500, or Kawasaki's parallel twins.)

USA (Harley Davidson's Evolution range, with a carburetter.)

Denmark (honorable mention for the x81c02 by Lego, though strictly speaking you can't ride it.)

Of course, there are countless other makes that come from places other than what I've just listed, but in all likelihood you don't have your heart set on a Nimbus (though you could go 'round the world on one!).

A word on "race replica" details: race numbers on a regular road-going bike are tacky. In general, don't monkey-mimic the great icons of motorcycling history: there was only one Steve Mc Queen, only one Barry Sheene. There is only one [insert name of favourite MotoGP rider], you're different, so within the boundaries of good taste, personalise your bike to show what you are about.
There are many "custom builders" out there setting some real trends. Some are questionable, others are the stuff that we've dreamed about since we were kids and that finally someone has put a blowtorch and an angle-grinder to. Figure out for yourself what looks good and harmonious and resist the temptation to "mix old and new": that almost never works. When in doubt, ask a pro: real enthusiasts should always be courteous and happy to talk about their craft.

In closing, let me draw your attention to something you don't hear about very often. This may sound strange but trust me when I say that you will be surprised to find out just how different your motorcycle feels once you take it out of its routine. What I mean by that is that you can know your machine inside out, ride the same commute or weekend trips for years, and then one day you're off on a ten-day trip, luggage, unknown territory... and you discover that it's like a significantly different bike. Not better, not worse, simply more than what you knew.  You'll get to exploit some previously untapped potential and discover just how much more your motorcycle can do. Whatever you end up buying, try to use it as much as you can, in as many different settings as you can, and always know this: it's your motorcycle, and it is the best one in the world.