It all started when I was leaving a Flight Lesson and a Twin Engine plane flew over with an awesome, deep, Throaty sound to it (what Twin has that kind of sound?).
Quite a few of them, actually. Anything that has a pair of large 6-cylinder engines will probably make what you could call a "throaty" sound.
1. Once I get my ASEL PPL How hard will it be to get my Multi-Engine License??
Depends how much money you have.
Seriously, once you really know your way around an airplane, the multi rating isn't too tough. I got mine in a weekend, and many others have as well. Being good and proficient, however, requires that you fly twins often, and they're expensive! In many cases, the airplane alone will be around $300/hr to rent, and instruction can cost another $50-75 (most FBO's charge more for advanced training). For me to rent the local twin costs $299, plus $50 for the instructor, plus tax. That's over $360/hr, which equates to SIX DOLLARS A MINUTE. I'm pretty sure it's literally cheaper to light money on fire. And yes, even though I'm rated I still have to pay an instructor to ride along - Rental minimums on twins are not low, in our case you need either 100 hours multi (That's $36,000+!) or you need 700 hours total time (which I have) and 25 in type (which I don't). So, for the next 19.4 hours I have to pay an instructor, and even once I can rent it solo it's still $300 + tax per hour.
2. How much harder is it to fly a Twin?
When things are going well: Not much, but there are more systems to be monitoring on a twin. For example: Cabin heat is provided by a heater rather than engine heat, since there's no engine in front of you. One advantage is that you can start the heater as soon as you've started the engines and the cabin will warm up much faster than on a single. The disadvantage is that you have to pay attention and not overheat it, so you have to turn the heat off and leave the fan blower on for a few minutes before you land. That's just one example, and there are quite a few others. The bottom line is that you need to have enough flying experience that you can easily stay ahead of the airplane, even with all of the extra knobology.
As far as the learning, there's a few more book things to learn. For example, you'll have some new V-speeds: Vmc is the minimum airspeed at which you can control the airplane on one engine and is marked as a red radial line on the airspeed indicator (just like Vne, only at the other end of the speed range). You'll also learn about the factors that affect Vmc. Another important one is Vyse, which is the best rate of climb airspeed with one engine inoperative (Vy Single Engine is what it stands for). That one is marked with a blue radial line on the airspeed indicator. Some twins will also have numbers for Vxse (best angle of climb with OEI) and Vsse (Safe Single Engine, minimum speed at which you should practice maneuvers intentionally OEI). There are also some additional performance charts in the POH, such as an accelerate-stop distance chart. That's the distance it takes to accelerate to takeoff speed, lose an engine, and stop. And, of course, you'll need to learn about all those extra systems I mentioned.
When things aren't going well, ie engine failure: Some twins are easier than others to fly on one. The Apache that I got my multi rating in is pretty easy on one engine, as it has large vertical tail surfaces and low-powered engines. At the other end of the spectrum would be something like an Aerostar, which is a high-powered, fire-breathing turbocharged beast that has tiny vertical tail surfaces. Even the slightest mistake on an Aerostar engine failure will put you out of control in a hurry.
3. What is a good Twin to use for Charter Piloting?
Depends on the mission, like others have said. A good one to start with would be a Seneca or Baron, they're relatively easy and economical to fly compared to a lot of other twins, they're easy to obtain, and they have nice large back doors for your passengers to get in and out without clambering onto wings or over seats. However, they're best for shorter-range missions, as neither one is going to break 200 knots. They also won't carry a huge load.
Moving up the scale - The speed scale, anyway - The aforementioned Aerostar, once you've tamed it, is a little bigger and quite a bit faster. It's about as fast as you're going to get on a piston-engine airplane, I think. Alternatively, the Cessna 400-series airplanes will go reasonably fast and carry several people quite nicely.
Any higher than that, you're talking turbine. I've always been particularly fond of the King Air 200's. They're good-looking airplanes, they'll go >250 knots, and they can land on amazingly short strips for an airplane of that size which gives them great utility. Plus, they're very comfortable, without the vibration inherent in piston-powered airplanes.
Then you're into jets, which could mean anything from the forthcoming PJ's and existing VLJ's all the way up to the Boeing Business Jets.
IIRC you're pretty young still and have a ways to go - I think the landscape will change a lot by the time you're actually flying charters. Many of the airplanes I've mentioned above or similar are on the way out. Nobody has manufactured a successful cabin-class piston twin since the mid-1980's, and that means those that are out there are getting long in the tooth and VERY expensive to maintain. That means that they're on the way out. I would bet a lot of them will be replaced with small jets - Or you may get your wish to fly single-engine, as the single-engine turboprops like the TBM's and PC12's take over the market that used to be served by piston twins.
IMHO, you could do very well by following in the footsteps of Tony Condon.