Pancake holster is a style. It has two belt loops, one on each side of the pouch. It is called pancake because it is relatively flat in profile, in other words, not having a held open receptacle the way, say, western holsters do.
Paddle holsters refer to the way the holster is carried. The paddle is essentially a large clip that goes inside the pants, while the holster stays outside the waistband.
There are several potential issues with paddle holsters. One is the tightness of the paddle against the pant waistband. I've seen videos where the gun was drawn and it came out still inside by the holster. Both the gun and the holster came out together. Tightness will obviously depend upon the thickness of the pant. Jeans, being thicker, could be expected to hold the holster down more tightly than a pair of dress pants.
Another problem is comfort. The paddle is a fairly large, rigid, shaped piece of nylon or kydex. It can dig into your abdomen in certain positions, especially sitting.
Another issue is related to the first one. Since the holster is held down only by the paddle, the pouch is likely to be less retentive and the handgun fit, looser. This could allow the firearm to unintentionally work its way out of the holster during bending, jumping, or other activity.
Personally I prefer my holster to be held down by a belt. I think this greatly reduces the issues mentioned above.
Left handedness is not a problem. Excellent custom holsters are available for under 150.00 Also, most major manufacturers make left handed holsters for just about every handgun. These will set you back less than 100.00 Look for Galco, Mitch Rosen, Alessi, and others.
At the bottom of the price scale are molded kydex holsters. These are very secure, form fitting, durable, and reliable. They will set you back less than 50.00 Retention force is adjustable via several screws. They are made with belt loops, or clips, for inside the waistband. These clips hold tighter than paddles across a waistband and will also clip over a belt, acting like a snug belt loop. They are available in both right and left handed versions.
I am right handed. I can wear a right handed version either inside my waistband or inside my belt, between it and my waistband. I also have several left handed kydex holsters that I wear clipped to my belt, on the outside my belt.
If you decide on a kydex holster, think about how you will wear it--inside your waistband, between your belt and your waistband, or outside your belt. And make sure you order the correct version.
One last point. Kydex holsters are inexpensive enough to order one or two just to see how you want to carry--IWB, OWB. Once you decide, you can purchase a leather one. Finally, you can fine tune the fit inside your kydex holster by heating it with a hairdryer and molding it to your specifications.
If you are going to open carry, you may want to consider one of the security holsters. These either have a loop that swings to hold in the back of the handgun, or they have an apparatus to hold the trigger guard until released by a button push. I believe that there is increased security for those who carry concealed vs open.
Remember, at least 10% of the LEOs who are killed in the line of duty are killed with their own guns.